Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic149 | C2 | semidirect |
| 3. #23749939 | C2 | semidirect |
| 4. #23749936 | C2 | semidirect |
| 5. #23749918 | C2 | semidirect |
| 6. #23749823 | C2 | semidirect |
| 7. #23749764 | C2 | semidirect |
| 8. #23749728 | C2 | semidirect |
| 9. #23749726 | C2 | semidirect |
| 10. #23749679 | C2 | semidirect |
| 11. #448×C149 | C2 | semidirect |
| 104. Q8×C149 | #41 | semidirect |
| 140. C149 | #3112 | semidirect |
| 149. #448 | D149 | semidirect |
| 229. Q8 | #14558735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750170 | 2 |
| C2×Q8×Dic149 | 2 |
| #23749939 | 2 |
| #23749936 | 2 |
| #23749918 | 2 |
| #23749823 | 2 |
| #23749764 | 2 |
| #23749728 | 2 |
| #23749726 | 2 |
| #23749679 | 2 |
| #448×C149 | 2 |
| #3112 | 149 |