Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
952 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 169 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, socle | C23×C71 | C24 |
| Fitting | #390×C71 | C2 |
| hypercenter | #390 | D71 |
| hypocenter | C71 | #2431 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11765864 | C2 | semidirect |
| 2. C2×#14556124 | C2 | semidirect |
| 3. C2×#14556116 | C2 | semidirect |
| 4. C2×#14556103 | C2 | semidirect |
| 5. #17985908 | C2 | semidirect |
| 6. #17985904 | C2 | semidirect |
| 7. #17985876 | C2 | semidirect |
| 8. C4×(C2×D71)⋊C4 | C2 | semidirect |
| 9. #390×C71 | C2 | semidirect |
| 38. C2×Dic142 | D4 | semidirect |
| 58. C2×C4×D71 | D4 | semidirect |
| 66. C2×D4×C71 | D4 | semidirect |
| 109. C2×Dic71 | #41 | semidirect |
| 149. C71 | #2431 | semidirect |
| 156. #390 | D71 | semidirect |
| 202. C2×D4 | D284 | semidirect |