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. #23750338 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23749951 | C2 | semidirect |
| 4. #23749949 | C2 | semidirect |
| 5. #23749914 | C2 | semidirect |
| 6. #23749862 | C2 | semidirect |
| 7. #23749861 | C2 | semidirect |
| 8. #23749707 | C2 | semidirect |
| 9. C8×C22⋊D149 | C2 | semidirect |
| 10. #23749662 | C2 | semidirect |
| 11. #427×C149 | C2 | semidirect |
| 120. C149 | #3341 | semidirect |
| 132. #427 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750338 | 2 |
| #23750029 | 2 |
| #23749951 | 2 |
| #23749949 | 2 |
| #23749914 | 2 |
| #23749862 | 2 |
| #23749861 | 2 |
| #23749707 | 2 |
| C8×C22⋊D149 | 2 |
| #23749662 | 2 |
| #427×C149 | 2 |
| #3341 | 149 |