Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23750180 | C2 | semidirect |
| 3. #23749935 | C2 | semidirect |
| 4. #23749927 | C2 | semidirect |
| 5. #23749917 | C2 | semidirect |
| 6. #23749911 | C2 | semidirect |
| 7. #23749905 | C2 | semidirect |
| 8. #23749660 | C2 | semidirect |
| 9. C4⋊C8×D149 | C2 | semidirect |
| 11. #476×C149 | C2 | semidirect |
| 44. #14558735 | Q8 | semidirect |
| 134. C149 | #3076 | semidirect |
| 141. #476 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| C4×#14558735 | 2 |
| #23749935 | 2 |
| #23749927 | 2 |
| #23749917 | 2 |
| #23749911 | 2 |
| #23749905 | 2 |
| #23749660 | 2 |
| C4⋊C8×D149 | 2 |
| #23749618 | 2 |
| #476×C149 | 2 |
| #3076 | 149 |