Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C22×C42×C71 | C2 |
| hypercenter | C22×C42 | D71 |
| hypocenter | C71 | #2854 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556111 | C2 | semidirect |
| 3. #17985901 | C2 | semidirect |
| 4. #17985897 | C2 | semidirect |
| 5. #17985890 | C2 | semidirect |
| 6. #17985878 | C2 | semidirect |
| 7. #17985859 | C2 | semidirect |
| 8. C22×C42×C71 | C2 | semidirect |
| 50. C22×C4×C71 | D4 | semidirect |
| 107. C4×C71 | #123 | semidirect |
| 118. C71 | #2854 | semidirect |
| 121. C22×C42 | D71 | semidirect |
| 160. C22×C4 | D284 | semidirect |
| 227. C4 | #14556111 | semidirect |