Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23754253 | C2 | semidirect |
| 3. #23754250 | C2 | semidirect |
| 4. #23754246 | C2 | semidirect |
| 5. #23754244 | C2 | semidirect |
| 6. #23754241 | C2 | semidirect |
| 7. #23754237 | C2 | semidirect |
| 9. C4×Dic614 | C2 | semidirect |
| 10. C4×C22⋊D307 | C2 | semidirect |
| 11. C4×C22⋊D307 | C2 | semidirect |
| 12. #23754219 | C2 | semidirect |
| 13. #23754217 | C2 | semidirect |
| 14. C2×C4×Dic307 | C2 | semidirect |
| 15. C4×D4×C307 | C2 | semidirect |
| 103. C307 | #529 | semidirect |
| 116. C4×D4 | D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754255 | 2 |
| #23754253 | 2 |
| #23754250 | 2 |
| #23754246 | 2 |
| #23754244 | 2 |
| #23754241 | 2 |
| #23754237 | 2 |
| #23754232 | 2 |
| C4×Dic614 | 2 |
| C4×C22⋊D307 | 2 |
| #23754219 | 2 |
| #23754217 | 2 |
| C2×C4×Dic307 | 2 |
| C4×D4×C307 | 2 |
| #529 | 307 |