Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
796 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 796 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #2670 |
| 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. C2×#14524032 | C2 | semidirect |
| 2. C2×#14524013 | C2 | semidirect |
| 3. #16863314 | C2 | semidirect |
| 4. #16863306 | C2 | semidirect |
| 5. #16863305 | C2 | semidirect |
| 6. #16863296 | C2 | semidirect |
| 7. #16863285 | C2 | semidirect |
| 8. #16863251 | C2 | semidirect |
| 9. #393×C67 | C2 | semidirect |
| 13. C22×D268 | C22 | semidirect |
| 17. C2×Dic67⋊C4 | C22 | semidirect |
| 23. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 26. C2×C4×Dic67 | C22 | semidirect |
| 27. C67⋊#95 | C22 | semidirect |
| 28. C22×Q8×C67 | C22 | semidirect |
| 31. #95×C67 | C22 | semidirect |
| 32. #95×C67 | C22 | semidirect |
| 61. (C2×D67)⋊C4 | D4 | semidirect |
| 158. C67 | #2670 | semidirect |
| 162. #393 | D67 | semidirect |
| 169. C22×Q8 | C2×D67 | semidirect |
| 189. #95 | C2×D67 | semidirect |
| 190. #95 | C2×D67 | semidirect |