Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#18011911 | C2 | semidirect |
| 3. #23750034 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749956 | C2 | semidirect |
| 7. #23749921 | C2 | semidirect |
| 8. #23749916 | C2 | semidirect |
| 9. #432×C149 | C2 | semidirect |
| 112. C149 | #3238 | semidirect |
| 122. #432 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011911 | 2 |
| #23750159 | 2 |
| #23750034 | 2 |
| #23749985 | 2 |
| #23749956 | 2 |
| #23749939 | 2 |
| #23749921 | 2 |
| #23749916 | 2 |
| #432×C149 | 2 |
| #3238 | 149 |