Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
522 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #401×C71 | C2 |
| hypercenter | #401 | D71 |
| hypocenter | C71 | #2825 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17985928 | C2 | semidirect |
| 2. #17985923 | C2 | semidirect |
| 3. #17985917 | C2 | semidirect |
| 4. #17985909 | C2 | semidirect |
| 5. #17985909 | C2 | semidirect |
| 6. #17985877 | C2 | semidirect |
| 7. #401×C71 | C2 | semidirect |
| 90. C71 | #2825 | semidirect |
| 91. #401 | D71 | semidirect |