Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
620 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #2635 |
| 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. C2×#14524017 | C2 | semidirect |
| 2. C2×C4×C22⋊D67 | C2 | semidirect |
| 3. #16863336 | C2 | semidirect |
| 4. #16863333 | C2 | semidirect |
| 5. #16863314 | C2 | semidirect |
| 6. #16863312 | C2 | semidirect |
| 7. #16863306 | C2 | semidirect |
| 8. #16863305 | C2 | semidirect |
| 9. #16863288 | C2 | semidirect |
| 10. #16863274 | C2 | semidirect |
| 11. #381×C67 | C2 | semidirect |
| 69. C22×C4×C67 | D4 | semidirect |
| 158. C67 | #2635 | semidirect |
| 169. #381 | D67 | semidirect |
| 216. C22×C4 | D268 | semidirect |