Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C4×Dic614 | C2 | semidirect |
| 3. #23754193 | C2 | semidirect |
| 4. #23754183 | C2 | semidirect |
| 6. #23754171 | C2 | semidirect |
| 9. #19096814 | C4 | semidirect |
| 21. Dic614 | C2×C4 | semidirect |
| 25. C307⋊C8 | C2×C4 | semidirect |
| 49. C307 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19096814 | 2 |
| C4×Dic614 | 2 |
| #23754193 | 2 |
| #23754183 | 2 |
| #23754181 | 2 |
| #23754171 | 2 |
| C4×D4×C307 | 2 |
| #440 | 307 |