Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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, socle | C23×C67 | C24 |
| Fitting | #384×C67 | C2 |
| hypercenter | #384 | D67 |
| hypocenter | C67 | #2542 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524042 | C2 | semidirect |
| 2. C2×#14524021 | C2 | semidirect |
| 4. #16863331 | C2 | semidirect |
| 7. #16863265 | C2 | semidirect |
| 8. C4×Dic67⋊C4 | C2 | semidirect |
| 9. #384×C67 | C2 | semidirect |
| 35. C2×D268 | Q8 | semidirect |
| 45. Dic67⋊C4 | D4 | semidirect |
| 100. C4×C67 | C22⋊Q8 | semidirect |
| 112. C67 | #2542 | semidirect |
| 120. #384 | D67 | semidirect |
| 216. C4 | #14524021 | semidirect |