Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
800 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #395×C71 | C2 |
| hypercenter | #395 | D71 |
| hypocenter | C71 | #2434 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556127 | C2 | semidirect |
| 4. #17985920 | C2 | semidirect |
| 5. #17985919 | C2 | semidirect |
| 6. #17985918 | C2 | semidirect |
| 7. #17985903 | C2 | semidirect |
| 11. #395×C71 | C2 | semidirect |
| 65. (C2×D71)⋊C4 | Q8 | semidirect |
| 95. C2×C4×C71 | C2×Q8 | semidirect |
| 108. C2×Dic71 | C2×Q8 | semidirect |
| 123. C2×D71 | C4⋊Q8 | semidirect |
| 141. C71 | #2434 | semidirect |
| 148. #395 | D71 | semidirect |
| 254. C2×C4 | Q8×D71 | semidirect |