Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C2×#120×C67 | C2 |
| hypercenter | C2×#120 | D67 |
| hypocenter | C67 | #2622 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic67 | C2 | semidirect |
| 2. #16863324 | C2 | semidirect |
| 3. #16863310 | C2 | semidirect |
| 4. #16863276 | C2 | semidirect |
| 5. #16863268 | C2 | semidirect |
| 6. #16863252 | C2 | semidirect |
| 9. C2×Dic67⋊C4 | C22 | semidirect |
| 14. C2×C22⋊Dic67 | C22 | semidirect |
| 15. C67⋊#95 | C22 | semidirect |
| 16. C67⋊#95 | C22 | semidirect |
| 98. C67 | #2622 | semidirect |