Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C22×C71 | C23×C4 |
| Fitting | #380×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #380 | D71 |
| hypocenter | C71 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556093 | C2 | semidirect |
| 3. #17985904 | C2 | semidirect |
| 4. #17985903 | C2 | semidirect |
| 10. C22×Dic142 | C4 | semidirect |
| 43. C22⋊Dic71 | Q8 | semidirect |
| 78. C2×Dic71 | C2×Q8 | semidirect |
| 81. Dic142 | C22⋊C4 | semidirect |
| 86. C22×C71 | C4×Q8 | semidirect |
| 106. C71 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #14556093 | semidirect |