Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750349 | C2 | semidirect |
| 3. #23749964 | C2 | semidirect |
| 4. #23749902 | C2 | semidirect |
| 5. #23749865 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 7. #23749790 | C2 | semidirect |
| 8. C4×#14558725 | C2 | semidirect |
| 9. C8×D596 | C2 | semidirect |
| 10. #23749620 | C2 | semidirect |
| 11. #487×C149 | C2 | semidirect |
| 125. C149 | #3302 | semidirect |
| 129. #487 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750349 | 2 |
| #23750278 | 2 |
| #23749964 | 2 |
| #23749902 | 2 |
| #23749865 | 2 |
| #23749832 | 2 |
| #23749790 | 2 |
| C4×#14558725 | 2 |
| C8×D596 | 2 |
| #23749620 | 2 |
| #487×C149 | 2 |
| #3302 | 149 |