Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C24×C67 |
| socle | C2×C67 | C22×D16 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C22×C4×C67 ◁ C22×C8×C67 ◁ C22×C16×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#508×C67 | C2 | semidirect |
| 2. C67×#2264 | C2 | semidirect |
| 3. C67×#2263 | C2 | semidirect |
| 4. C67×#2262 | C2 | semidirect |
| 5. C2×M64×C67 | C2 | semidirect |
| 10. #508×C67 | C22 | semidirect |
| 11. C2×Q32×C67 | C22 | semidirect |
| 13. C2×D16×C67 | C22 | semidirect |
| 15. Q64×C67 | C22 | semidirect |
| 16. SD64×C67 | C22 | semidirect |
| 17. D32×C67 | C22 | semidirect |
| 18. M64×C67 | C22 | semidirect |
| 19. C2×C32×C67 | C22 | semidirect |
| 89. #33981 | C67 | direct (N × H) |
| 94. C2×#508 | C2×C67 | semidirect |
| 95. #2264 | C2×C67 | semidirect |
| 96. #2263 | C2×C67 | semidirect |
| 97. #2262 | C2×C67 | semidirect |
| 98. C2×M64 | C2×C67 | semidirect |
| 99. C67 | #33981 | direct (N × H) |
| 104. #508 | C22×C67 | semidirect |
| 105. C2×Q32 | C22×C67 | semidirect |
| 107. C2×D16 | C22×C67 | semidirect |
| 109. Q64 | C22×C67 | semidirect |
| 110. SD64 | C22×C67 | semidirect |
| 111. D32 | C22×C67 | semidirect |
| 112. M64 | C22×C67 | semidirect |
| 113. C2×C32 | C22×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508×C67 | 2 |
| C67×#2264 | 2 |
| C67×#2263 | 2 |
| C67×#2262 | 2 |
| C2×M64×C67 | 2 |
| #33981 | 67 |