Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #400×C71 | C2 |
| hypercenter | #400 | D71 |
| hypocenter | C71 | #2396 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556093 | C2 | semidirect |
| 4. #17985933 | C2 | semidirect |
| 6. #17985919 | C2 | semidirect |
| 8. #17985850 | C2 | semidirect |
| 9. #17985850 | C2 | semidirect |
| 11. #400×C71 | C2 | semidirect |
| 47. C2×C4×D71 | Q8 | semidirect |
| 129. C71 | #2396 | semidirect |
| 132. #400 | D71 | semidirect |