Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #23750230 | C2 | semidirect |
| 2. #23750024 | C2 | semidirect |
| 3. #23750001 | C2 | semidirect |
| 4. #23749991 | C2 | semidirect |
| 5. #23749989 | C2 | semidirect |
| 6. #23749876 | C2 | semidirect |
| 7. #23749859 | C2 | semidirect |
| 8. #23749735 | C2 | semidirect |
| 9. C4×#14558721 | C2 | semidirect |
| 10. #23749581 | C2 | semidirect |
| 11. #540×C149 | C2 | semidirect |
| 114. C149 | #3176 | semidirect |
| 117. #540 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750230 | 2 |
| #23750024 | 2 |
| #23750001 | 2 |
| #23749991 | 2 |
| #23749989 | 2 |
| #23749876 | 2 |
| #23749859 | 2 |
| #23749735 | 2 |
| C4×#14558721 | 2 |
| #23749581 | 2 |
| #540×C149 | 2 |
| #3176 | 149 |