Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4⋊Q8×D149 | C2 | semidirect |
| 3. #23750018 | C2 | semidirect |
| 4. #23749992 | C2 | semidirect |
| 5. #23749835 | C2 | semidirect |
| 6. #23749831 | C2 | semidirect |
| 7. #23749827 | C2 | semidirect |
| 8. #23749779 | C2 | semidirect |
| 10. #23749681 | C2 | semidirect |
| 11. #462×C149 | C2 | semidirect |
| 139. C149 | #3218 | semidirect |
| 146. #462 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D149 | 2 |
| #23750162 | 2 |
| #23750018 | 2 |
| #23749992 | 2 |
| #23749835 | 2 |
| #23749831 | 2 |
| #23749827 | 2 |
| #23749779 | 2 |
| #23749765 | 2 |
| #23749681 | 2 |
| #462×C149 | 2 |
| #3218 | 149 |