Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16863304 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #535×C67 | C2 |
| socle | C2×C67 | #392 |
| hypercenter | #535 | D67 |
| hypocenter | C67 | #2008 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864194 | C2 | semidirect |
| 2. C2×#14524069 | C2 | semidirect |
| 3. #16863413 | C2 | semidirect |
| 4. #16863401 | C2 | semidirect |
| 5. #16863369 | C2 | semidirect |
| 6. #16863166 | C2 | semidirect |
| 7. #535×C67 | C2 | semidirect |
| 35. C2×Dic134 | D4 | semidirect |
| 36. C2×D268 | D4 | semidirect |
| 48. #11761612 | D4 | semidirect |
| 50. C2×C67⋊C8 | D4 | semidirect |
| 143. C67 | #2008 | semidirect |
| 146. #535 | D67 | semidirect |