Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1224 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 368 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C137 | C23 |
| commutator | C22 | C23×C4×C137 |
| Frattini, cosocle | C23 | C24×C137 |
| socle | C23×C137 | C24 |
| prime radical | C2×#120×C137 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C4×C137 | C2 | semidirect |
| 3. C2×C4×D4×C137 | C2 | semidirect |
| 4. #386×C137 | C2 | semidirect |
| 5. #385×C137 | C2 | semidirect |
| 6. #379×C137 | C2 | semidirect |
| 7. C4×C22⋊C4×C137 | C2 | semidirect |
| 13. C23×C4×C137 | C22 | semidirect |
| 14. #120×C137 | C4 | direct (N × H) |
| 16. C2×C4⋊C4×C137 | C22 | semidirect |
| 20. C2×C22⋊C4×C137 | C22 | semidirect |
| 21. C2×C42×C137 | C22 | semidirect |
| 22. #95×C137 | C22 | semidirect |
| 25. C24×C137 | C2×C4 | semidirect |
| 30. C2×D4×C137 | C2×C4 | semidirect |
| 36. C22×C4×C137 | D4 | semidirect |
| 46. C22⋊C4×C137 | C2×C4 | semidirect |
| 56. C23×C137 | C22×C4 | semidirect |
| 70. C2×C4×C137 | C22×C4 | semidirect |
| 81. C22×C137 | C4×D4 | semidirect |
| 89. C4×C137 | #120 | direct (N × H) |
| 95. C137 | C4×#120 | direct (N × H) |
| 96. C4×#120 | C137 | direct (N × H) |
| 97. C24×C4 | C2×C137 | semidirect |
| 99. C2×C4×D4 | C2×C137 | semidirect |
| 100. #386 | C2×C137 | semidirect |
| 101. #385 | C2×C137 | semidirect |
| 102. #379 | C2×C137 | semidirect |
| 103. C4×C22⋊C4 | C2×C137 | semidirect |
| 109. C23×C4 | C22×C137 | semidirect |
| 110. #120 | C4×C137 | direct (N × H) |
| 112. C2×C4⋊C4 | C22×C137 | semidirect |
| 116. C2×C22⋊C4 | C22×C137 | semidirect |
| 117. C2×C42 | C22×C137 | semidirect |
| 118. #95 | C22×C137 | semidirect |
| 121. C24 | C2×C4×C137 | semidirect |
| 126. C2×D4 | C2×C4×C137 | semidirect |
| 132. C22×C4 | D4×C137 | semidirect |
| 142. C22⋊C4 | C2×C4×C137 | semidirect |
| 152. C23 | C22×C4×C137 | semidirect |
| 166. C2×C4 | C22×C4×C137 | semidirect |
| 177. C22 | C4×D4×C137 | semidirect |
| 185. C4 | #120×C137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C137 | 2 |
| C2×#120×C137 | 2 |
| C2×C4×D4×C137 | 2 |
| #386×C137 | 2 |
| #385×C137 | 2 |
| #379×C137 | 2 |
| C4×C22⋊C4×C137 | 2 |
| C4×#120 | 137 |