Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#18011834 | C2 | semidirect |
| 5. C2×#18011829 | C2 | semidirect |
| 6. #23749389 | C2 | semidirect |
| 7. #343×C149 | C2 | semidirect |
| 11. #18011944 | C4 | semidirect |
| 116. C149 | #1908 | semidirect |
| 123. #343 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011944 | 2 |
| C2×#18011919 | 2 |
| #23749624 | 2 |
| C2×#18011834 | 2 |
| C2×#18011829 | 2 |
| #23749389 | 2 |
| #343×C149 | 2 |
| #1908 | 149 |