Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #23750027 | C2 | semidirect |
| 3. #23749993 | C2 | semidirect |
| 6. #23749732 | C2 | semidirect |
| 7. Q16×Dic149 | C2 | semidirect |
| 9. #494×C149 | C2 | semidirect |
| 78. C149 | #3177 | semidirect |
| 82. #494 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750236 | 2 |
| #23750027 | 2 |
| #23749993 | 2 |
| #23749880 | 2 |
| #23749863 | 2 |
| #23749732 | 2 |
| Q16×Dic149 | 2 |
| #23749579 | 2 |
| #494×C149 | 2 |
| #3177 | 149 |