Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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×D367 |
| commutator, socle, cosocle | C22×C367 | C24 |
| Fitting | #126×C367 | C2 |
| prime radical | C2×C22⋊D367 | C22 |
| hypercenter | #126 | D367 |
| hypocenter | C367 | #556 |
| LCS | G ▷ C22×C367 ▷ C367 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26044260 | C2 | semidirect |
| 2. #26044256 | C2 | semidirect |
| 3. #26044256 | C2 | semidirect |
| 4. #26044254 | C2 | semidirect |
| 7. #26044239 | C2 | semidirect |
| 8. #26044238 | C2 | semidirect |
| 9. C4×Dic734 | C2 | semidirect |
| 10. #26044226 | C2 | semidirect |
| 11. #26044226 | C2 | semidirect |
| 13. #26044218 | C2 | semidirect |
| 14. #26044217 | C2 | semidirect |
| 15. #126×C367 | C2 | semidirect |
| 97. C367 | #556 | semidirect |
| 103. #126 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044260 | 2 |
| #26044256 | 2 |
| #26044254 | 2 |
| #26044247 | 2 |
| #26044239 | 2 |
| #26044238 | 2 |
| C4×Dic734 | 2 |
| #26044226 | 2 |
| (C22⋊D367)⋊C4 | 2 |
| #26044218 | 2 |
| #26044217 | 2 |
| #126×C367 | 2 |
| #556 | 367 |