Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23750032 | C2 | semidirect |
| 3. #23749928 | C2 | semidirect |
| 4. #23749922 | C2 | semidirect |
| 5. #23749904 | C2 | semidirect |
| 6. #23749755 | C2 | semidirect |
| 9. #499×C149 | C2 | semidirect |
| 41. D1192 | Q8 | semidirect |
| 96. C149 | #3389 | semidirect |
| 100. #499 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750331 | 2 |
| #23750032 | 2 |
| #23749928 | 2 |
| #23749922 | 2 |
| #23749904 | 2 |
| #23749755 | 2 |
| #23749736 | 2 |
| C4×D1192 | 2 |
| #499×C149 | 2 |
| #3389 | 149 |