Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
628 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #383×C71 | C2 |
| hypercenter | #383 | D71 |
| hypocenter | C71 | #2631 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556116 | C2 | semidirect |
| 2. C2×C4×D284 | C2 | semidirect |
| 3. #17985926 | C2 | semidirect |
| 4. #17985912 | C2 | semidirect |
| 5. #17985909 | C2 | semidirect |
| 6. #17985909 | C2 | semidirect |
| 7. #17985877 | C2 | semidirect |
| 8. #383×C71 | C2 | semidirect |
| 52. C42×C71 | D4 | semidirect |
| 109. C71 | #2631 | semidirect |
| 117. #383 | D71 | semidirect |
| 161. C42 | D284 | semidirect |