Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #123×C367 | C2 |
| prime radical | C2×D4×C367 | C22 |
| hypercenter | #123 | D367 |
| hypocenter | C367 | #552 |
| LCS | G ▷ C22×C367 ▷ C367 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26044254 | C2 | semidirect |
| 2. #26044254 | C2 | semidirect |
| 3. #26044252 | C2 | semidirect |
| 4. #26044251 | C2 | semidirect |
| 5. #26044251 | C2 | semidirect |
| 7. #26044238 | C2 | semidirect |
| 8. #26044238 | C2 | semidirect |
| 9. #26044226 | C2 | semidirect |
| 11. #26044220 | C2 | semidirect |
| 12. #26044217 | C2 | semidirect |
| 13. #26044217 | C2 | semidirect |
| 14. C2×Dic367⋊C4 | C2 | semidirect |
| 97. C367 | #552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044254 | 2 |
| #26044252 | 2 |
| #26044251 | 2 |
| #26044242 | 2 |
| #26044238 | 2 |
| #26044226 | 2 |
| D4×Dic367 | 2 |
| #26044220 | 2 |
| #26044217 | 2 |
| C2×Dic367⋊C4 | 2 |
| #123×C367 | 2 |
| #552 | 367 |