Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750347 | C2 | semidirect |
| 4. #23750003 | C2 | semidirect |
| 5. #23749850 | C2 | semidirect |
| 6. #23749847 | C2 | semidirect |
| 7. #23749829 | C2 | semidirect |
| 8. C8×Dic298 | C2 | semidirect |
| 9. #23749719 | C2 | semidirect |
| 11. C4×Q16×C149 | C2 | semidirect |
| 114. C149 | #3393 | semidirect |
| 125. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750347 | 2 |
| #23750010 | 2 |
| #23750009 | 2 |
| #23750003 | 2 |
| #23749850 | 2 |
| #23749847 | 2 |
| #23749829 | 2 |
| C8×Dic298 | 2 |
| #23749719 | 2 |
| #23749707 | 2 |
| C4×Q16×C149 | 2 |
| #3393 | 149 |