Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750290 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23749904 | C2 | semidirect |
| 4. #23749902 | C2 | semidirect |
| 5. C8×Dic298 | C2 | semidirect |
| 8. #500×C149 | C2 | semidirect |
| 34. D1192 | Q8 | semidirect |
| 51. Dic298 | D8 | semidirect |
| 53. D596 | C2×Q8 | semidirect |
| 66. C8×C149 | C2×Q8 | semidirect |
| 83. C149 | Q8×D8 | semidirect |
| 87. #500 | D149 | semidirect |
| 150. C8 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750290 | 2 |
| #23750029 | 2 |
| #23749904 | 2 |
| #23749902 | 2 |
| C8×Dic298 | 2 |
| C4×D1192 | 2 |
| #23749707 | 2 |
| #500×C149 | 2 |
| Q8×D8 | 149 |