Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 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 | C22×C71 | C22×C8 |
| Fitting | C2×C4⋊C8×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D71 |
| hypocenter | C71 | #1923 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C8×Dic71 | C2 | semidirect |
| 5. #17985754 | C2 | semidirect |
| 6. #17985753 | C2 | semidirect |
| 7. C2×C4⋊C8×C71 | C2 | semidirect |
| 40. (C2×D71)⋊C4 | C8 | semidirect |
| 123. C71 | #1923 | semidirect |
| 124. C2×C4⋊C8 | D71 | semidirect |