Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊Q8×D149 | C2 | semidirect |
| 3. #23749987 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749984 | C2 | semidirect |
| 6. #23749974 | C2 | semidirect |
| 7. #23749970 | C2 | semidirect |
| 8. #23749625 | C2 | semidirect |
| 9. #23749623 | C2 | semidirect |
| 10. #23749577 | C2 | semidirect |
| 11. #489×C149 | C2 | semidirect |
| 140. C149 | #3141 | semidirect |
| 147. #489 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750174 | 2 |
| C4⋊Q8×D149 | 2 |
| #23749987 | 2 |
| #23749985 | 2 |
| #23749984 | 2 |
| #23749974 | 2 |
| #23749970 | 2 |
| #23749625 | 2 |
| #23749623 | 2 |
| #23749577 | 2 |
| #489×C149 | 2 |
| #3141 | 149 |