Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1088 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1088 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 | C23×D4×C67 | C2 |
| hypercenter | C23×D4 | D67 |
| hypocenter | C67 | #2435 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524030 | C2 | semidirect |
| 2. C2×#14524022 | C2 | semidirect |
| 3. #16863310 | C2 | semidirect |
| 4. #16863299 | C2 | semidirect |
| 5. #16863252 | C2 | semidirect |
| 6. C4×C22⋊Dic67 | C2 | semidirect |
| 8. C22×Dic134 | C22 | semidirect |
| 11. C2×C4⋊Dic67 | C22 | semidirect |
| 12. C2×Dic67⋊C4 | C22 | semidirect |
| 15. C2×C22⋊Dic67 | C22 | semidirect |
| 16. C2×C22⋊Dic67 | C22 | semidirect |
| 17. C2×C4×Dic67 | C22 | semidirect |
| 18. C67⋊#95 | C22 | semidirect |
| 91. C22×C67 | #124 | semidirect |
| 108. C67 | #2435 | semidirect |
| 199. C22 | #14524030 | semidirect |