Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #393×C67 | C2 |
| hypercenter | #393 | D67 |
| hypocenter | C67 | #2824 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863338 | C2 | semidirect |
| 2. #16863323 | C2 | semidirect |
| 3. #16863314 | C2 | semidirect |
| 4. #16863312 | C2 | semidirect |
| 5. #16863307 | C2 | semidirect |
| 7. #16863273 | C2 | semidirect |
| 8. #16863268 | C2 | semidirect |
| 9. #393×C67 | C2 | semidirect |
| 127. C67 | #2824 | semidirect |
| 133. #393 | D67 | semidirect |