Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14524029 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #410×C67 | C2 |
| socle | C2×C67 | #393 |
| hypercenter | #410 | D67 |
| hypocenter | C67 | #2031 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #410 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863949 | C2 | semidirect |
| 4. #16863166 | C2 | semidirect |
| 5. #16863155 | C2 | semidirect |
| 6. #16863152 | C2 | semidirect |
| 44. C2×Q8×C67 | Q8 | semidirect |
| 46. C2×D4×C67 | Q8 | semidirect |
| 103. C67 | #2031 | semidirect |
| 131. C2×Q8 | Dic134 | semidirect |
| 133. C2×D4 | Dic134 | semidirect |