Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #23750160 | C2 | semidirect |
| 2. #23750009 | C2 | semidirect |
| 3. #23749982 | C2 | semidirect |
| 4. #23749867 | C2 | semidirect |
| 6. #23749855 | C2 | semidirect |
| 7. #23749719 | C2 | semidirect |
| 8. #23749712 | C2 | semidirect |
| 9. #23749707 | C2 | semidirect |
| 10. C4×C8×D149 | C2 | semidirect |
| 11. #499×C149 | C2 | semidirect |
| 118. C149 | #3168 | semidirect |
| 121. #499 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750160 | 2 |
| #23750009 | 2 |
| #23749982 | 2 |
| #23749867 | 2 |
| #23749862 | 2 |
| #23749855 | 2 |
| #23749719 | 2 |
| #23749712 | 2 |
| #23749707 | 2 |
| C4×C8×D149 | 2 |
| #499×C149 | 2 |
| #3168 | 149 |