Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #500×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #500 | D67 |
| hypocenter | C67 | Q8×D8 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864061 | C2 | semidirect |
| 2. #16863800 | C2 | semidirect |
| 3. #16863675 | C2 | semidirect |
| 4. #16863673 | C2 | semidirect |
| 5. C8×Dic134 | C2 | semidirect |
| 8. #500×C67 | C2 | semidirect |
| 34. D536 | Q8 | semidirect |
| 59. D268 | C2×Q8 | semidirect |
| 63. Dic134 | D8 | semidirect |
| 65. C8×C67 | C2×Q8 | semidirect |
| 84. C67 | Q8×D8 | semidirect |
| 87. #500 | D67 | semidirect |
| 150. C8 | Q8×D67 | semidirect |