Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | C2×#124×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C2×#124 | D67 |
| hypocenter | C67 | #2326 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic67 | C2 | semidirect |
| 3. #16863303 | C2 | semidirect |
| 5. #16863289 | C2 | semidirect |
| 6. #16863271 | C2 | semidirect |
| 7. #16863266 | C2 | semidirect |
| 8. #16863242 | C2 | semidirect |
| 27. #124×C67 | C4 | semidirect |
| 49. C2×Q8×C67 | C2×C4 | semidirect |
| 56. C22⋊C4×C67 | C2×C4 | semidirect |
| 57. C42×C67 | C2×C4 | semidirect |
| 112. C67 | #2326 | semidirect |
| 125. #124 | Dic67 | semidirect |
| 145. C2×Q8 | C2×Dic67 | semidirect |
| 165. C22⋊C4 | C2×Dic67 | semidirect |
| 169. C42 | C2×Dic67 | semidirect |