Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23749902 | C2 | semidirect |
| 3. #23749704 | C2 | semidirect |
| 4. #23749378 | C2 | semidirect |
| 5. #23749371 | C2 | semidirect |
| 6. #23749369 | C2 | semidirect |
| 7. #492×C149 | C2 | semidirect |
| 65. C8×C149 | D8 | semidirect |
| 85. C149 | #1685 | semidirect |
| 87. #492 | D149 | semidirect |
| 151. C8 | #14558721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749902 | 2 |
| #23749817 | 2 |
| #23749704 | 2 |
| #23749378 | 2 |
| #23749371 | 2 |
| #23749369 | 2 |
| #492×C149 | 2 |
| #1685 | 149 |