Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750331 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23750026 | C2 | semidirect |
| 4. #23749924 | C2 | semidirect |
| 5. #23749922 | C2 | semidirect |
| 6. #23749914 | C2 | semidirect |
| 7. C8×Dic298 | C2 | semidirect |
| 11. #499×C149 | C2 | semidirect |
| 45. D1192 | Q8 | semidirect |
| 108. C149 | #3380 | semidirect |
| 113. #499 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750331 | 2 |
| #23750029 | 2 |
| #23750026 | 2 |
| #23749924 | 2 |
| #23749922 | 2 |
| #23749914 | 2 |
| C8×Dic298 | 2 |
| C4×D1192 | 2 |
| #23749707 | 2 |
| #499×C149 | 2 |
| #3380 | 149 |