Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23749641 | C2 | semidirect |
| 3. #23749621 | C2 | semidirect |
| 4. #23749593 | C2 | semidirect |
| 5. #23749396 | C2 | semidirect |
| 6. #23749389 | C2 | semidirect |
| 7. #568×C149 | C2 | semidirect |
| 10. #18011941 | C4 | semidirect |
| 12. #18011936 | C4 | semidirect |
| 118. C149 | #1881 | semidirect |
| 121. #568 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750423 | 2 |
| #23749641 | 2 |
| #23749621 | 2 |
| #23749593 | 2 |
| #23749396 | 2 |
| #23749389 | 2 |
| #568×C149 | 2 |
| #1881 | 149 |