Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23750028 | C2 | semidirect |
| 3. #23750004 | C2 | semidirect |
| 4. #23749977 | C2 | semidirect |
| 5. #23749975 | C2 | semidirect |
| 7. C4×#14558726 | C2 | semidirect |
| 79. C2×C4×C149 | Q16 | semidirect |
| 104. C149 | #3170 | 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 |
| #23750028 | 2 |
| #23750004 | 2 |
| #23749977 | 2 |
| #23749975 | 2 |
| #23749864 | 2 |
| C4×#14558726 | 2 |
| C2×C4×#11924746 | 2 |
| #533×C149 | 2 |
| #3170 | 149 |