Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #386×C67 | C2 |
| hypercenter | #386 | D67 |
| hypocenter | C67 | #2669 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524039 | C2 | semidirect |
| 2. C2×#14524017 | C2 | semidirect |
| 3. C2×#14524013 | C2 | semidirect |
| 4. C2×#14524011 | C2 | semidirect |
| 5. #16863312 | C2 | semidirect |
| 6. #16863306 | C2 | semidirect |
| 7. #16863305 | C2 | semidirect |
| 8. #16863288 | C2 | semidirect |
| 9. #386×C67 | C2 | semidirect |
| 13. C22×D268 | C22 | semidirect |
| 16. C22×C22⋊D67 | C22 | semidirect |
| 21. C2×C4⋊Dic67 | C22 | semidirect |
| 26. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 27. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 28. C2×C4×Dic67 | C22 | semidirect |
| 29. C67⋊#95 | C22 | semidirect |
| 31. C23×C4×C67 | C22 | semidirect |
| 33. C2×C22⋊C4×C67 | C22 | semidirect |
| 34. #95×C67 | C22 | semidirect |
| 68. (C2×D67)⋊C4 | D4 | semidirect |
| 74. C2×D4×C67 | D4 | semidirect |
| 180. C67 | #2669 | semidirect |
| 189. #386 | D67 | semidirect |
| 198. C23×C4 | C2×D67 | semidirect |
| 211. C2×C22⋊C4 | C2×D67 | semidirect |
| 214. #95 | C2×D67 | semidirect |
| 244. C2×D4 | D268 | semidirect |