Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22⋊C4 |
| commutator | C22 | C2×C42×C17 |
| Frattini, cosocle | C24 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C4 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C22⋊C4×C17 | C2 | semidirect |
| 4. C17×#342 | C2 | semidirect |
| 6. C23×C4×C17 | C4 | semidirect |
| 10. C2×C4⋊C4×C17 | C4 | semidirect |
| 11. C2×C22⋊C4×C17 | C4 | semidirect |
| 15. C2×C42×C17 | C4 | semidirect |
| 16. C17×#99 | C4 | direct (N × H) |
| 39. C22⋊C4×C17 | C2×C4 | semidirect |
| 49. C23×C17 | C42 | semidirect |
| 70. C2×C4×C17 | C42 | semidirect |
| 74. C4×#99 | C17 | direct (N × H) |
| 96. C4×C17 | #99 | direct (N × H) |
| 99. C4×C22⋊C4 | C2×C17 | semidirect |
| 100. #342 | C2×C17 | semidirect |
| 109. C23×C4 | C4×C17 | semidirect |
| 113. C2×C4⋊C4 | C4×C17 | semidirect |
| 114. C2×C22⋊C4 | C4×C17 | semidirect |
| 118. C2×C42 | C4×C17 | semidirect |
| 119. #99 | C4×C17 | direct (N × H) |
| 121. C17 | C4×#99 | direct (N × H) |
| 143. C22⋊C4 | C2×C4×C17 | semidirect |
| 153. C23 | C42×C17 | semidirect |
| 174. C2×C4 | C42×C17 | semidirect |
| 199. C4 | C17×#99 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C17 | 2 |
| C2×C17×#99 | 2 |
| C4×C22⋊C4×C17 | 2 |
| C17×#342 | 2 |
| C4×#99 | 17 |