Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23750180 | C2 | semidirect |
| 3. #23749965 | C2 | semidirect |
| 4. #23749921 | C2 | semidirect |
| 5. #23749915 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 8. #23749729 | C2 | semidirect |
| 9. #23749726 | C2 | semidirect |
| 10. #23749681 | C2 | semidirect |
| 11. #461×C149 | C2 | semidirect |
| 136. C149 | #3116 | semidirect |
| 144. #461 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| C4×#14558735 | 2 |
| #23749965 | 2 |
| #23749921 | 2 |
| #23749915 | 2 |
| #23749832 | 2 |
| #23749784 | 2 |
| #23749729 | 2 |
| #23749726 | 2 |
| #23749681 | 2 |
| #461×C149 | 2 |
| #3116 | 149 |