Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #379×C67 | C2 |
| hypercenter | #379 | D67 |
| hypocenter | C67 | #2613 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D67 | C2 | semidirect |
| 2. C2×#14524027 | C2 | semidirect |
| 3. C2×#14524013 | C2 | semidirect |
| 4. C2×#14524012 | C2 | semidirect |
| 5. #16863312 | C2 | semidirect |
| 6. #16863305 | C2 | semidirect |
| 7. #16863257 | C2 | semidirect |
| 8. #16863251 | C2 | semidirect |
| 9. #379×C67 | C2 | semidirect |
| 11. C22×D268 | C22 | semidirect |
| 17. C22×C22⋊D67 | C22 | semidirect |
| 22. C2×C4⋊Dic67 | C22 | semidirect |
| 24. C2×C22⋊Dic67 | C22 | semidirect |
| 25. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 27. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 28. C67⋊#95 | C22 | semidirect |
| 32. C2×C22⋊C4×C67 | C22 | semidirect |
| 36. C23×D67 | D4 | semidirect |
| 52. C22×Dic67 | D4 | semidirect |
| 65. C24×C67 | D4 | semidirect |
| 155. C67 | #2613 | semidirect |
| 164. #379 | D67 | semidirect |
| 186. C2×C22⋊C4 | C2×D67 | semidirect |
| 197. C24 | D268 | semidirect |