Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23750334 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23750027 | C2 | semidirect |
| 4. #23750026 | C2 | semidirect |
| 5. #23749927 | C2 | semidirect |
| 6. #23749925 | C2 | semidirect |
| 7. #23749913 | C2 | semidirect |
| 8. C8×Dic298 | C2 | semidirect |
| 61. D8×C149 | Q8 | semidirect |
| 108. C149 | #3380 | semidirect |
| 154. D8 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750334 | 2 |
| #23750029 | 2 |
| #23750027 | 2 |
| #23750026 | 2 |
| #23749927 | 2 |
| #23749925 | 2 |
| #23749913 | 2 |
| C8×Dic298 | 2 |
| D8×Dic149 | 2 |
| C4×D8×C149 | 2 |
| #3380 | 149 |