Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23749920 | C2 | semidirect |
| 3. #23749917 | C2 | semidirect |
| 5. #23749835 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 78. C2×C4×C149 | Q16 | semidirect |
| 104. C149 | #3249 | semidirect |
| 182. C2×C4 | #14558726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| #23749920 | 2 |
| #23749917 | 2 |
| #23749864 | 2 |
| #23749835 | 2 |
| #23749832 | 2 |
| C2×C4⋊#11924746 | 2 |
| #533×C149 | 2 |
| #3249 | 149 |