Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 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. #23750175 | C2 | semidirect |
| 2. #23750028 | C2 | semidirect |
| 3. #23750001 | C2 | semidirect |
| 4. #23749973 | C2 | semidirect |
| 5. #23749971 | C2 | semidirect |
| 6. #23749859 | C2 | semidirect |
| 7. C4×#14558721 | C2 | semidirect |
| 8. C2×C4×#11924746 | C2 | semidirect |
| 9. #532×C149 | C2 | semidirect |
| 77. #11924746 | #41 | semidirect |
| 89. C2×C4×C149 | D8 | semidirect |
| 120. C149 | #3169 | semidirect |
| 123. #532 | D149 | semidirect |
| 208. C2×C4 | #14558721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750028 | 2 |
| #23750001 | 2 |
| #23749973 | 2 |
| #23749971 | 2 |
| #23749859 | 2 |
| C4×#14558721 | 2 |
| C2×C4×#11924746 | 2 |
| #532×C149 | 2 |
| #3169 | 149 |