Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | #386×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #386 | D71 |
| hypocenter | C71 | #2366 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C22⋊D71 | C2 | semidirect |
| 3. C2×(C22⋊D71)⋊C4 | C2 | semidirect |
| 4. #17985899 | C2 | semidirect |
| 5. #17985899 | C2 | semidirect |
| 6. #17985879 | C2 | semidirect |
| 7. #17985877 | C2 | semidirect |
| 8. #17985850 | C2 | semidirect |
| 9. #386×C71 | C2 | semidirect |
| 15. #14556124 | C4 | semidirect |
| 37. C2×D284 | C2×C4 | semidirect |
| 42. C2×C22⋊D71 | C2×C4 | semidirect |
| 43. C2×C22⋊D71 | C2×C4 | semidirect |
| 53. Dic71⋊C4 | D4 | semidirect |
| 61. C4×Dic71 | C2×C4 | semidirect |
| 66. C2×D4×C71 | C2×C4 | semidirect |
| 144. Dic71 | C4×D4 | semidirect |
| 154. C71 | #2366 | semidirect |
| 162. #386 | D71 | semidirect |
| 202. C2×D4 | C4×D71 | semidirect |