Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556097 |
| commutator | C42×C71 | C23 |
| Frattini | C42 | C22×D71 |
| Fitting | #557×C71 | C2 |
| socle | C22×C71 | #120 |
| hypercenter | #557 | D71 |
| hypocenter | C71 | #1626 |
| LCS | G ▷ C42×C71 ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #557 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #17985745 | C2 | semidirect |
| 5. Q8⋊(C71⋊C8) | C2 | semidirect |
| 6. Q8⋊(C71⋊C8) | C2 | semidirect |
| 7. #557×C71 | C2 | semidirect |
| 55. Q8×C71 | SD16 | semidirect |
| 91. C71 | #1626 | semidirect |
| 92. #557 | D71 | semidirect |
| 146. Q8 | #11765852 | semidirect |