Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | #424×C71 | C2 |
| hypercenter | #424 | D71 |
| hypocenter | C71 | #2923 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986059 | C2 | semidirect |
| 3. #17986055 | C2 | semidirect |
| 4. #17986026 | C2 | semidirect |
| 7. M16×Dic71 | C2 | semidirect |
| 8. C2×#14556038 | C2 | semidirect |
| 9. #424×C71 | C2 | semidirect |
| 94. C71 | #2923 | semidirect |
| 99. #424 | D71 | semidirect |