Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #23750033 | C2 | semidirect |
| 4. #23750032 | C2 | semidirect |
| 5. #23750027 | C2 | semidirect |
| 6. #23750024 | C2 | semidirect |
| 7. #23750024 | C2 | semidirect |
| 11. #499×C149 | C2 | semidirect |
| 43. #14558719 | Q8 | semidirect |
| 44. #14558719 | Q8 | semidirect |
| 99. C149 | #3166 | semidirect |
| 108. #499 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750181 | 2 |
| #125×D149 | 2 |
| #23750033 | 2 |
| #23750032 | 2 |
| #23750027 | 2 |
| #23750024 | 2 |
| #23749666 | 2 |
| #23749664 | 2 |
| C4×#14558719 | 2 |
| #499×C149 | 2 |
| #3166 | 149 |