Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #405×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #2951 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863876 | C2 | semidirect |
| 3. #16863498 | C2 | semidirect |
| 4. C4×Dic268 | C2 | semidirect |
| 5. C4×D536 | C2 | semidirect |
| 6. C2×#14523977 | C2 | semidirect |
| 7. #16863398 | C2 | semidirect |
| 8. #405×C67 | C2 | semidirect |
| 10. #14524065 | C4 | semidirect |
| 30. #11761628 | C2×C4 | semidirect |
| 37. Dic268 | C2×C4 | semidirect |
| 38. #11761617 | C2×C4 | semidirect |
| 39. D536 | C2×C4 | semidirect |
| 47. C2×C8×C67 | C2×C4 | semidirect |
| 96. C67 | #2951 | semidirect |
| 104. #405 | D67 | semidirect |
| 138. C2×C8 | C4×D67 | semidirect |