Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 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. #23750321 | C2 | semidirect |
| 2. #23750027 | C2 | semidirect |
| 3. #23749950 | C2 | semidirect |
| 4. #23749939 | C2 | semidirect |
| 5. #23749926 | C2 | semidirect |
| 6. #23749878 | C2 | semidirect |
| 7. C4×D1192 | C2 | semidirect |
| 8. #23749667 | C2 | semidirect |
| 9. #436×C149 | C2 | semidirect |
| 102. C149 | #3355 | semidirect |
| 111. #436 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750321 | 2 |
| #23750027 | 2 |
| #23749950 | 2 |
| #23749939 | 2 |
| #23749926 | 2 |
| #23749878 | 2 |
| C4×D1192 | 2 |
| #23749667 | 2 |
| #436×C149 | 2 |
| #3355 | 149 |