Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C4⋊Dic307 | C2 | semidirect |
| 3. #23754185 | C2 | semidirect |
| 4. #23754182 | C2 | semidirect |
| 5. C2×M16×C307 | C2 | semidirect |
| 7. #19096826 | C4 | semidirect |
| 20. Dic614 | C2×C4 | semidirect |
| 22. D1228 | C2×C4 | semidirect |
| 51. C307 | #417 | semidirect |
| 54. C2×M16 | D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19096826 | 2 |
| C2×C4⋊Dic307 | 2 |
| #23754185 | 2 |
| #23754182 | 2 |
| C2×M16×C307 | 2 |
| #417 | 307 |