Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
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×D307 |
| commutator, socle, cosocle | C22×C307 | C24 |
| Fitting | #126×C307 | C2 |
| prime radical | C2×C22⋊D307 | C22 |
| hypercenter | #126 | D307 |
| hypocenter | C307 | #563 |
| LCS | G ▷ C22×C307 ▷ C307 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23754260 | C2 | semidirect |
| 2. #23754259 | C2 | semidirect |
| 3. #23754255 | C2 | semidirect |
| 4. #23754254 | C2 | semidirect |
| 5. #23754253 | C2 | semidirect |
| 6. #23754251 | C2 | semidirect |
| 7. #23754250 | C2 | semidirect |
| 11. #23754240 | C2 | semidirect |
| 12. #23754238 | C2 | semidirect |
| 13. #23754237 | C2 | semidirect |
| 14. #23754237 | C2 | semidirect |
| 15. #126×C307 | C2 | semidirect |
| 97. C307 | #563 | semidirect |
| 104. #126 | D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754260 | 2 |
| #23754259 | 2 |
| #23754255 | 2 |
| #23754254 | 2 |
| #23754253 | 2 |
| #23754251 | 2 |
| #23754250 | 2 |
| #23754246 | 2 |
| #23754244 | 2 |
| #23754242 | 2 |
| #23754240 | 2 |
| #23754238 | 2 |
| #23754237 | 2 |
| #126×C307 | 2 |
| #563 | 307 |