Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
630 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #394×C67 | C2 |
| hypercenter | #394 | D67 |
| hypocenter | C67 | #2818 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524039 | C2 | semidirect |
| 2. C2×#14524038 | C2 | semidirect |
| 3. #16863313 | C2 | semidirect |
| 4. #16863312 | C2 | semidirect |
| 5. #16863311 | C2 | semidirect |
| 6. #16863306 | C2 | semidirect |
| 7. #16863305 | C2 | semidirect |
| 8. #16863305 | C2 | semidirect |
| 9. #16863304 | C2 | semidirect |
| 10. #16863263 | C2 | semidirect |
| 11. #394×C67 | C2 | semidirect |
| 66. C4×Dic67 | D4 | semidirect |
| 164. C67 | #2818 | semidirect |
| 170. #394 | D67 | semidirect |