Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750341 | C2 | semidirect |
| 2. #23750340 | C2 | semidirect |
| 3. #23750028 | C2 | semidirect |
| 4. #23749951 | C2 | semidirect |
| 5. #23749948 | C2 | semidirect |
| 6. #23749916 | C2 | semidirect |
| 7. #23749860 | C2 | semidirect |
| 8. C4×#14558721 | C2 | semidirect |
| 9. #23749690 | C2 | semidirect |
| 10. #23749660 | C2 | semidirect |
| 11. #476×C149 | C2 | semidirect |
| 125. C149 | #3341 | semidirect |
| 133. #476 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750341 | 2 |
| #23750340 | 2 |
| #23750028 | 2 |
| #23749951 | 2 |
| #23749948 | 2 |
| #23749916 | 2 |
| #23749860 | 2 |
| C4×#14558721 | 2 |
| #23749690 | 2 |
| #23749660 | 2 |
| #476×C149 | 2 |
| #3341 | 149 |