Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750182 | C2 | semidirect |
| 3. #23749967 | C2 | semidirect |
| 4. #23749921 | C2 | semidirect |
| 5. #23749916 | C2 | semidirect |
| 6. #23749836 | C2 | semidirect |
| 7. #23749831 | C2 | semidirect |
| 9. #23749733 | C2 | semidirect |
| 10. #23749727 | C2 | semidirect |
| 11. #432×C149 | C2 | semidirect |
| 136. C149 | #3116 | semidirect |
| 148. #432 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| C4×#14558736 | 2 |
| #23749967 | 2 |
| #23749921 | 2 |
| #23749916 | 2 |
| #23749836 | 2 |
| #23749831 | 2 |
| #23749789 | 2 |
| #23749733 | 2 |
| #23749727 | 2 |
| #432×C149 | 2 |
| #3116 | 149 |