Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23754259 | C2 | semidirect |
| 2. #23754255 | C2 | semidirect |
| 3. #23754253 | C2 | semidirect |
| 5. #23754236 | C2 | semidirect |
| 6. Q8×Dic307 | C2 | semidirect |
| 7. #23754225 | C2 | semidirect |
| 9. #23754219 | C2 | semidirect |
| 10. #23754218 | C2 | semidirect |
| 11. C22⋊Q8×C307 | C2 | semidirect |
| 72. C307 | #556 | semidirect |
| 79. C22⋊Q8 | D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754259 | 2 |
| #23754255 | 2 |
| #23754253 | 2 |
| #23754246 | 2 |
| #23754236 | 2 |
| Q8×Dic307 | 2 |
| #23754225 | 2 |
| C4×C22⋊D307 | 2 |
| #23754219 | 2 |
| #23754218 | 2 |
| C22⋊Q8×C307 | 2 |
| #556 | 307 |