Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16863275 |
| commutator | C2×C4×C67 | C22×C4 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #568×C67 | C2 |
| socle | C2×C67 | #386 |
| hypercenter | #568 | D67 |
| hypocenter | C67 | #1902 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16863406 | C2 | semidirect |
| 4. C2×#14523961 | C2 | semidirect |
| 5. #16863168 | C2 | semidirect |
| 6. C67⋊#338 | C2 | semidirect |
| 11. C2×#11761618 | C4 | semidirect |
| 12. C2×#11761616 | C4 | semidirect |
| 108. C67 | #1902 | semidirect |