Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
724 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #398×C67 | C2 |
| hypercenter | #398 | D67 |
| hypocenter | C67 | #2543 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #398 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524018 | C2 | semidirect |
| 2. C2×#14524018 | C2 | semidirect |
| 3. C2×#14524005 | C2 | semidirect |
| 4. #16863322 | C2 | semidirect |
| 5. #16863313 | C2 | semidirect |
| 6. #16863306 | C2 | semidirect |
| 7. #16863286 | C2 | semidirect |
| 8. #16863274 | C2 | semidirect |
| 9. #16863274 | C2 | semidirect |
| 10. #95×D67 | C2 | semidirect |
| 11. #398×C67 | C2 | semidirect |
| 51. C2×D268 | D4 | semidirect |
| 61. C2×C4×D67 | D4 | semidirect |
| 162. C67 | #2543 | semidirect |
| 166. #398 | D67 | semidirect |