Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17985879 |
| commutator | C2×C4×C71 | C22×C4 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #535×C71 | C2 |
| socle | C2×C71 | #386 |
| hypercenter | #535 | D71 |
| hypocenter | C71 | #1911 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986474 | C2 | semidirect |
| 2. #17986016 | C2 | semidirect |
| 3. C2×#14556045 | C2 | semidirect |
| 4. #17985755 | C2 | semidirect |
| 14. #127×C71 | C4 | semidirect |
| 15. #124×C71 | C4 | semidirect |
| 26. C4×Dic71 | D4 | semidirect |
| 30. C2×Q8×C71 | C2×C4 | semidirect |
| 36. C2×D4×C71 | C2×C4 | semidirect |
| 43. C42×C71 | C2×C4 | semidirect |
| 89. C71 | #1911 | semidirect |
| 98. #127 | Dic71 | semidirect |
| 99. #124 | Dic71 | semidirect |
| 111. C2×Q8 | C2×Dic71 | semidirect |
| 117. C2×D4 | C2×Dic71 | semidirect |
| 132. C42 | C2×Dic71 | semidirect |