Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1348 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 193 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 | C2×#127×C67 | C2 |
| hypercenter | C2×#127 | D67 |
| hypocenter | C67 | #2433 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×D67 | C2 | semidirect |
| 2. C2×#14524039 | C2 | semidirect |
| 3. C2×#14524014 | C2 | semidirect |
| 4. C2×#14524011 | C2 | semidirect |
| 5. #16863304 | C2 | semidirect |
| 6. #16863299 | C2 | semidirect |
| 7. #16863298 | C2 | semidirect |
| 8. C4×(C2×D67)⋊C4 | C2 | semidirect |
| 9. C2×#127×C67 | C2 | semidirect |
| 14. C22×C22⋊D67 | C22 | semidirect |
| 22. C2×C4⋊Dic67 | C22 | semidirect |
| 23. C2×C22⋊Dic67 | C22 | semidirect |
| 24. C2×C22⋊Dic67 | C22 | semidirect |
| 26. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 27. C2×C4×Dic67 | C22 | semidirect |
| 28. C67⋊#95 | C22 | semidirect |
| 30. C22×D4×C67 | C22 | semidirect |
| 31. C22×D4×C67 | C22 | semidirect |
| 33. C2×C42×C67 | C22 | semidirect |
| 43. C2×D268 | D4 | semidirect |
| 58. C2×C4×D67 | D4 | semidirect |
| 63. (C2×D67)⋊C4 | D4 | semidirect |
| 75. C2×D4×C67 | D4 | semidirect |
| 113. C2×C4×C67 | C2×D4 | semidirect |
| 124. C2×Dic67 | C2×D4 | semidirect |
| 152. C2×D67 | #127 | semidirect |
| 154. C4×C67 | #120 | semidirect |
| 168. C67 | #2433 | semidirect |
| 171. C2×#127 | D67 | semidirect |
| 187. C22×D4 | C2×D67 | semidirect |
| 188. C22×D4 | C2×D67 | semidirect |
| 200. C2×C42 | C2×D67 | semidirect |
| 231. C2×D4 | C22⋊D67 | semidirect |
| 293. C2×C4 | D4×D67 | semidirect |
| 325. C4 | #14524011 | semidirect |