Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 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 | #379×C67 | C2 |
| hypercenter | #379 | D67 |
| hypocenter | C67 | #2848 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524020 | C2 | semidirect |
| 3. #16863271 | C2 | semidirect |
| 4. #16863268 | C2 | semidirect |
| 5. #16863254 | C2 | semidirect |
| 8. C22×Dic134 | C22 | semidirect |
| 13. C2×C4⋊Dic67 | C22 | semidirect |
| 14. C2×Dic67⋊C4 | C22 | semidirect |
| 15. C2×Dic67⋊C4 | C22 | semidirect |
| 18. C67⋊#95 | C22 | semidirect |
| 39. C24×C67 | Q8 | semidirect |
| 71. C22×C67 | C22⋊Q8 | semidirect |
| 86. C67 | #2848 | semidirect |
| 110. C24 | Dic134 | semidirect |
| 157. C22 | #14524020 | semidirect |