Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #441×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #441 | D67 |
| hypocenter | C67 | #2943 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#11761629 | C2 | semidirect |
| 3. #16863509 | C2 | semidirect |
| 4. #16863507 | C2 | semidirect |
| 5. #16863503 | C2 | semidirect |
| 6. #16863499 | C2 | semidirect |
| 7. #16863494 | C2 | semidirect |
| 8. #16863431 | C2 | semidirect |
| 9. #16863391 | C2 | semidirect |
| 10. #97×D67 | C2 | semidirect |
| 11. #441×C67 | C2 | semidirect |
| 13. #14524066 | C4 | semidirect |
| 41. #11761629 | C2×C4 | semidirect |
| 49. #11761615 | C2×C4 | semidirect |
| 50. D536 | C2×C4 | semidirect |
| 54. C8×D67 | C2×C4 | semidirect |
| 65. Q16×C67 | C2×C4 | semidirect |
| 115. C67 | #2943 | semidirect |
| 121. #441 | D67 | semidirect |
| 165. Q16 | C4×D67 | semidirect |