Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23754255 | C2 | semidirect |
| 2. #23754251 | C2 | semidirect |
| 3. #23754250 | C2 | semidirect |
| 5. #23754240 | C2 | semidirect |
| 6. #23754239 | C2 | semidirect |
| 7. #23754225 | C2 | semidirect |
| 9. #23754219 | C2 | semidirect |
| 10. #23754218 | C2 | semidirect |
| 11. C2×C4⋊C4×C307 | C2 | semidirect |
| 72. C307 | #552 | semidirect |
| 84. C2×C4⋊C4 | D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754255 | 2 |
| #23754251 | 2 |
| #23754250 | 2 |
| #23754243 | 2 |
| #23754240 | 2 |
| #23754239 | 2 |
| #23754225 | 2 |
| C4×C22⋊D307 | 2 |
| #23754219 | 2 |
| #23754218 | 2 |
| C2×C4⋊C4×C307 | 2 |
| #552 | 307 |