Finite Group DatabasebetaFinite Group DatabasebetaOrder 8384.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D131 |
| commutator, socle | C22×C131 | C24 |
| Fitting | #126×C131 | C2 |
| hypercenter | #126 | D131 |
| hypocenter | C131 | #563 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16862246 | C2 | semidirect |
| 2. #16862245 | C2 | semidirect |
| 3. #16862241 | C2 | semidirect |
| 4. #16862240 | C2 | semidirect |
| 5. #16862239 | C2 | semidirect |
| 6. #16862237 | C2 | semidirect |
| 7. #16862236 | C2 | semidirect |
| 11. #16862226 | C2 | semidirect |
| 12. #16862224 | C2 | semidirect |
| 13. #16862223 | C2 | semidirect |
| 14. #16862223 | C2 | semidirect |
| 15. #126×C131 | C2 | semidirect |
| 97. C131 | #563 | semidirect |
| 104. #126 | D131 | semidirect |