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 | #381×C67 | C2 |
| hypercenter | #381 | D67 |
| hypocenter | C67 | #2613 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D268 | C2 | semidirect |
| 2. C2×#14524026 | C2 | semidirect |
| 3. C2×#14524013 | C2 | semidirect |
| 4. #16863314 | C2 | semidirect |
| 5. #16863306 | C2 | semidirect |
| 6. #16863251 | C2 | semidirect |
| 7. #381×C67 | C2 | semidirect |
| 12. C22×D268 | C22 | semidirect |
| 16. C2×Dic67⋊C4 | C22 | semidirect |
| 18. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 19. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 23. #95×C67 | C22 | semidirect |
| 27. C23×D67 | D4 | semidirect |
| 46. C22×C4×C67 | D4 | semidirect |
| 104. C67 | #2613 | semidirect |
| 110. #381 | D67 | semidirect |
| 127. #95 | C2×D67 | semidirect |
| 145. C22×C4 | D268 | semidirect |