Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 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 | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | #380×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #380 | D67 |
| hypocenter | C67 | #2377 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863296 | C2 | semidirect |
| 3. #16863286 | C2 | semidirect |
| 4. #16863281 | C2 | semidirect |
| 5. #16863274 | C2 | semidirect |
| 6. #16863272 | C2 | semidirect |
| 7. #16863267 | C2 | semidirect |
| 8. #16863259 | C2 | semidirect |
| 9. #380×C67 | C2 | semidirect |
| 13. #14524017 | C4 | semidirect |
| 37. C2×C22⋊D67 | C2×C4 | semidirect |
| 44. C4⋊Dic67 | C2×C4 | semidirect |
| 50. (C2×D67)⋊C4 | C2×C4 | semidirect |
| 54. C22×C4×C67 | C2×C4 | semidirect |
| 130. C67 | #2377 | semidirect |
| 139. #380 | D67 | semidirect |
| 176. C22×C4 | C4×D67 | semidirect |