Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #2849 |
| 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. C24×Dic67 | C2 | semidirect |
| 2. C2×#14524027 | C2 | semidirect |
| 4. #16863273 | C2 | semidirect |
| 5. #16863271 | C2 | semidirect |
| 6. #16863257 | C2 | semidirect |
| 7. #379×C67 | C2 | semidirect |
| 16. C2×C4⋊Dic67 | C22 | semidirect |
| 19. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 20. C67⋊#95 | C22 | semidirect |
| 34. C22×Dic67 | D4 | semidirect |
| 84. C22×C67 | #123 | semidirect |
| 102. C67 | #2849 | semidirect |
| 109. #379 | D67 | semidirect |
| 189. C22 | #14524027 | semidirect |