Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #23750361 | C2 | semidirect |
| 2. #23750349 | C2 | semidirect |
| 3. #23750006 | C2 | semidirect |
| 4. #23749845 | C2 | semidirect |
| 5. #23749842 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 8. C8×Dic298 | C2 | semidirect |
| 9. C4×#14558725 | C2 | semidirect |
| 10. SD16×Dic149 | C2 | semidirect |
| 11. #492×C149 | C2 | semidirect |
| 125. C149 | #3394 | semidirect |
| 130. #492 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750361 | 2 |
| #23750349 | 2 |
| #23750006 | 2 |
| #23749845 | 2 |
| #23749842 | 2 |
| #23749832 | 2 |
| #23749817 | 2 |
| C8×Dic298 | 2 |
| C4×#14558725 | 2 |
| SD16×Dic149 | 2 |
| #492×C149 | 2 |
| #3394 | 149 |