Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C16 | C22⋊D71 |
| commutator | C4×C71 | C22×C8 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | #504×C71 | C2 |
| socle | C2×C71 | C8×D4 |
| hypercenter | #504 | D71 |
| hypocenter | C71 | #2170 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986415 | C2 | semidirect |
| 3. #17985819 | C2 | semidirect |
| 4. #17985784 | C2 | semidirect |
| 5. #17985783 | C2 | semidirect |
| 6. C16×Dic71 | C2 | semidirect |
| 7. #504×C71 | C2 | semidirect |
| 72. C71 | #2170 | semidirect |
| 74. #504 | D71 | semidirect |