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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23754259 | C2 | semidirect |
| 2. #23754258 | C2 | semidirect |
| 3. #23754255 | C2 | semidirect |
| 4. #23754255 | C2 | semidirect |
| 5. #23754253 | C2 | semidirect |
| 6. #23754253 | C2 | semidirect |
| 7. #23754251 | C2 | semidirect |
| 8. #23754250 | C2 | semidirect |
| 12. #23754239 | C2 | semidirect |
| 13. #23754238 | C2 | semidirect |
| 14. #23754236 | C2 | semidirect |
| 15. C22⋊Q8×C307 | C2 | semidirect |
| 97. C307 | #563 | semidirect |
| 113. 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 |
| #23754258 | 2 |
| #23754255 | 2 |
| #23754253 | 2 |
| #23754251 | 2 |
| #23754250 | 2 |
| #23754246 | 2 |
| #23754243 | 2 |
| #23754242 | 2 |
| #23754239 | 2 |
| #23754238 | 2 |
| #23754236 | 2 |
| C22⋊Q8×C307 | 2 |
| #563 | 307 |