Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
128 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556086 |
| commutator | C2×C4×C71 | C22×C4 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | #364×C71 | C2 |
| socle | C2×C71 | #432 |
| hypercenter | #364 | D71 |
| hypocenter | C71 | #2165 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #364 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17985820 | C2 | semidirect |
| 4. #17985776 | C2 | semidirect |
| 5. #364×C71 | C2 | semidirect |
| 54. C71 | #2165 | semidirect |
| 57. #364 | D71 | semidirect |