Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #23749920 | C2 | semidirect |
| 3. #23749902 | C2 | semidirect |
| 4. #23749873 | C2 | semidirect |
| 5. #23749827 | C2 | semidirect |
| 6. #23749825 | C2 | semidirect |
| 7. #23749649 | C2 | semidirect |
| 8. #533×C149 | C2 | semidirect |
| 112. C149 | #3254 | semidirect |
| 114. #533 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23749920 | 2 |
| #23749902 | 2 |
| #23749873 | 2 |
| #23749827 | 2 |
| #23749825 | 2 |
| #23749649 | 2 |
| #533×C149 | 2 |
| #3254 | 149 |