Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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 | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #442×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #442 | D67 |
| hypocenter | C67 | #3184 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863943 | C2 | semidirect |
| 2. #16863793 | C2 | semidirect |
| 3. #16863771 | C2 | semidirect |
| 4. #16863741 | C2 | semidirect |
| 5. #16863650 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863646 | C2 | semidirect |
| 8. #16863509 | C2 | semidirect |
| 9. #16863506 | C2 | semidirect |
| 10. #16863348 | C2 | semidirect |
| 11. #442×C67 | C2 | semidirect |
| 94. C8×C67 | #41 | semidirect |
| 96. C67⋊C8 | #41 | semidirect |
| 119. C67 | #3184 | semidirect |
| 129. #442 | D67 | semidirect |
| 215. C8 | #11761628 | semidirect |