Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 1. #23750182 | C2 | semidirect |
| 2. #23750021 | C2 | semidirect |
| 3. #23749997 | C2 | semidirect |
| 4. #23749977 | C2 | semidirect |
| 5. #23749971 | C2 | semidirect |
| 6. #23749852 | C2 | semidirect |
| 7. C4×#14558724 | C2 | semidirect |
| 8. C2×C4×#11924746 | C2 | semidirect |
| 72. #11924746 | #41 | semidirect |
| 84. C2×C4×C149 | SD16 | semidirect |
| 112. C149 | #3167 | semidirect |
| 195. C2×C4 | #14558724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| #23750021 | 2 |
| #23749997 | 2 |
| #23749977 | 2 |
| #23749971 | 2 |
| #23749852 | 2 |
| C4×#14558724 | 2 |
| C2×C4×#11924746 | 2 |
| #532×C149 | 2 |
| #3167 | 149 |