Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16863272 |
| commutator | C2×C4×C67 | C22×C4 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #421×C67 | C2 |
| socle | C2×C67 | #386 |
| hypercenter | #421 | D67 |
| hypocenter | C67 | #1905 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863873 | C2 | semidirect |
| 3. #16863406 | C2 | semidirect |
| 5. #16863168 | C2 | semidirect |
| 6. #16863152 | C2 | semidirect |
| 11. C2×#11761618 | C4 | semidirect |
| 12. C2×#11761616 | C4 | semidirect |
| 110. C67 | #1905 | semidirect |