Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
964 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 964 conjugacy classes of subgroups — too many to draw. Only its 553 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. Q8×Dic298 | C2 | semidirect |
| 2. #23750354 | C2 | semidirect |
| 3. #23750351 | C2 | semidirect |
| 35. C2×Q8×C149 | Q8 | semidirect |
| 70. C149 | #3502 | semidirect |
| 98. C2×Q8 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic298 | 2 |
| #23750354 | 2 |
| #23750351 | 2 |
| #23750256 | 2 |
| #23750182 | 2 |
| #23750103 | 2 |
| C2×C4×Q8×C149 | 2 |
| #3502 | 149 |