Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23749929 | C2 | semidirect |
| 3. #23749922 | C2 | semidirect |
| 4. #23749917 | C2 | semidirect |
| 5. #23749902 | C2 | semidirect |
| 6. #23749668 | C2 | semidirect |
| 7. C2×#18011844 | C2 | semidirect |
| 8. #23749652 | C2 | semidirect |
| 11. #544×C149 | C2 | semidirect |
| 42. #14558736 | Q8 | semidirect |
| 123. C149 | #3083 | semidirect |
| 125. #544 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750105 | 2 |
| #23749929 | 2 |
| #23749922 | 2 |
| #23749917 | 2 |
| #23749902 | 2 |
| #23749668 | 2 |
| C2×#18011844 | 2 |
| #23749652 | 2 |
| #23749624 | 2 |
| #23749619 | 2 |
| #544×C149 | 2 |
| #3083 | 149 |