Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
364 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 364 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. #23750340 | C2 | semidirect |
| 2. #23750028 | C2 | semidirect |
| 3. #23749949 | C2 | semidirect |
| 4. #23749946 | C2 | semidirect |
| 5. #23749915 | C2 | semidirect |
| 6. #23749912 | C2 | semidirect |
| 7. #23749859 | C2 | semidirect |
| 8. C4×#14558721 | C2 | semidirect |
| 9. D4×#11924746 | C2 | semidirect |
| 10. #23749661 | C2 | semidirect |
| 11. #555×C149 | C2 | semidirect |
| 125. C149 | #3341 | semidirect |
| 128. #555 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750340 | 2 |
| #23750028 | 2 |
| #23749949 | 2 |
| #23749946 | 2 |
| #23749915 | 2 |
| #23749912 | 2 |
| #23749859 | 2 |
| C4×#14558721 | 2 |
| D4×#11924746 | 2 |
| #23749661 | 2 |
| #555×C149 | 2 |
| #3341 | 149 |