Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 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. #23750336 | C2 | semidirect |
| 2. #23750332 | C2 | semidirect |
| 3. #23750028 | C2 | semidirect |
| 4. #23750025 | C2 | semidirect |
| 5. #23749927 | C2 | semidirect |
| 6. #23749924 | C2 | semidirect |
| 7. #23749916 | C2 | semidirect |
| 8. #23749749 | C2 | semidirect |
| 11. #476×C149 | C2 | semidirect |
| 47. #14558721 | Q8 | semidirect |
| 119. C149 | #3380 | semidirect |
| 128. #476 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750336 | 2 |
| #23750332 | 2 |
| #23750028 | 2 |
| #23750025 | 2 |
| #23749927 | 2 |
| #23749924 | 2 |
| #23749916 | 2 |
| #23749749 | 2 |
| C4×#14558721 | 2 |
| #23749705 | 2 |
| #476×C149 | 2 |
| #3380 | 149 |