Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 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 | #1851 |
| 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 |
|---|---|---|
| 2. C2×C4⋊(C71⋊C8) | C2 | semidirect |
| 3. C2×Dic71⋊C8 | C2 | semidirect |
| 6. #17985753 | C2 | semidirect |
| 7. #336×C71 | C2 | semidirect |
| 70. C2×C4×C71 | M16 | semidirect |
| 85. C2×Dic71 | M16 | semidirect |
| 126. C71 | #1851 | semidirect |
| 133. #336 | D71 | semidirect |
| 209. C2×C4 | #11765848 | semidirect |