Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #2555 |
| 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. C2×#14556114 | C2 | semidirect |
| 2. C2×#14556101 | C2 | semidirect |
| 3. #17985919 | C2 | semidirect |
| 4. #17985916 | C2 | semidirect |
| 5. #17985907 | C2 | semidirect |
| 6. #17985887 | C2 | semidirect |
| 7. #17985875 | C2 | semidirect |
| 8. C4×(C2×D71)⋊C4 | C2 | semidirect |
| 9. #390×C71 | C2 | semidirect |
| 55. (C2×D71)⋊C4 | D4 | semidirect |
| 143. C71 | #2555 | semidirect |
| 149. #390 | D71 | semidirect |