Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750345 | C2 | semidirect |
| 2. #23750028 | C2 | semidirect |
| 3. #23749960 | C2 | semidirect |
| 4. #23749946 | C2 | semidirect |
| 5. #23749907 | C2 | semidirect |
| 6. #23749905 | C2 | semidirect |
| 7. #23749869 | C2 | semidirect |
| 8. C4×#14558724 | C2 | semidirect |
| 9. #23749703 | C2 | semidirect |
| 10. #23749665 | C2 | semidirect |
| 82. #11924746 | #41 | semidirect |
| 122. C149 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750345 | 2 |
| #23750028 | 2 |
| #23749960 | 2 |
| #23749946 | 2 |
| #23749907 | 2 |
| #23749905 | 2 |
| #23749869 | 2 |
| C4×#14558724 | 2 |
| #23749703 | 2 |
| #23749665 | 2 |
| #547×C149 | 2 |
| #3353 | 149 |