Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
620 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 131 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 | #400×C67 | C2 |
| hypercenter | #400 | D67 |
| hypocenter | C67 | #2635 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524018 | C2 | semidirect |
| 2. C2×#14524005 | C2 | semidirect |
| 3. #16863331 | C2 | semidirect |
| 4. #16863314 | C2 | semidirect |
| 5. #16863313 | C2 | semidirect |
| 6. #16863306 | C2 | semidirect |
| 7. #16863306 | C2 | semidirect |
| 8. #16863285 | C2 | semidirect |
| 9. #16863274 | C2 | semidirect |
| 10. #16863258 | C2 | semidirect |
| 11. #400×C67 | C2 | semidirect |
| 57. C2×C4×D67 | D4 | semidirect |
| 158. C67 | #2635 | semidirect |
| 161. #400 | D67 | semidirect |