Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18011903 | C2 | semidirect |
| 3. #23750027 | C2 | semidirect |
| 4. #23749980 | C2 | semidirect |
| 5. #23749961 | C2 | semidirect |
| 6. #23749956 | C2 | semidirect |
| 9. #23749933 | C2 | semidirect |
| 10. #23749926 | C2 | semidirect |
| 11. #431×C149 | C2 | semidirect |
| 125. C149 | #3232 | semidirect |
| 137. #431 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750159 | 2 |
| C2×#18011903 | 2 |
| #23750027 | 2 |
| #23749980 | 2 |
| #23749961 | 2 |
| #23749956 | 2 |
| #23749944 | 2 |
| #23749939 | 2 |
| #23749933 | 2 |
| #23749926 | 2 |
| #431×C149 | 2 |
| #3232 | 149 |