Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C22×C4 |
| Fitting | #336×C71 | C2 |
| hypercenter | #336 | D71 |
| hypocenter | C71 | #1870 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11765848 | C2 | semidirect |
| 3. C2×(C2×D71)⋊C8 | C2 | semidirect |
| 4. C2×(C2×D71)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D71)⋊C8 | C2 | semidirect |
| 6. #17985754 | C2 | semidirect |
| 7. #336×C71 | C2 | semidirect |
| 52. C2×C71⋊C8 | D4 | semidirect |
| 64. C2×C8×C71 | D4 | semidirect |
| 81. C22×D71 | M16 | semidirect |
| 87. C2×C4×C71 | M16 | semidirect |
| 152. C71 | #1870 | semidirect |
| 159. #336 | D71 | semidirect |
| 213. C2×C8 | D284 | semidirect |
| 254. C2×C4 | #11765848 | semidirect |