Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
644 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 644 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 | #392×C67 | C2 |
| hypercenter | #392 | D67 |
| hypocenter | C67 | #2815 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524016 | C2 | semidirect |
| 2. C2×#14524014 | C2 | semidirect |
| 3. #16863324 | C2 | semidirect |
| 4. #16863323 | C2 | semidirect |
| 5. #16863321 | C2 | semidirect |
| 6. #16863305 | C2 | semidirect |
| 7. #16863304 | C2 | semidirect |
| 8. #16863304 | C2 | semidirect |
| 9. #16863304 | C2 | semidirect |
| 10. #16863258 | C2 | semidirect |
| 11. #392×C67 | C2 | semidirect |
| 56. C2×C4×D67 | D4 | semidirect |
| 169. C67 | #2815 | semidirect |
| 179. #392 | D67 | semidirect |