Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
364 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #23749752 | C2 | semidirect |
| 3. #23749749 | C2 | semidirect |
| 25. C2×#11924746 | Q8 | semidirect |
| 67. C149 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| #23749752 | 2 |
| #23749749 | 2 |
| #23749653 | 2 |
| #23749583 | 2 |
| C2×C4×#11924746 | 2 |
| #423×C149 | 2 |
| #2960 | 149 |