Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #499×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #499 | D67 |
| hypocenter | C67 | #3380 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #499 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864102 | C2 | semidirect |
| 2. #16863800 | C2 | semidirect |
| 3. #16863797 | C2 | semidirect |
| 4. #16863695 | C2 | semidirect |
| 5. #16863693 | C2 | semidirect |
| 6. #16863685 | C2 | semidirect |
| 7. C8×Dic134 | C2 | semidirect |
| 11. #499×C67 | C2 | semidirect |
| 45. D536 | Q8 | semidirect |
| 109. C67 | #3380 | semidirect |
| 113. #499 | D67 | semidirect |