Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750253 | C2 | semidirect |
| 3. #23749994 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749980 | C2 | semidirect |
| 6. #23749976 | C2 | semidirect |
| 7. #23749635 | C2 | semidirect |
| 10. C2×#18011836 | C2 | semidirect |
| 11. #405×C149 | C2 | semidirect |
| 127. C149 | #3137 | semidirect |
| 139. #405 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750253 | 2 |
| #23750201 | 2 |
| #23749994 | 2 |
| #23749985 | 2 |
| #23749980 | 2 |
| #23749976 | 2 |
| #23749635 | 2 |
| #23749627 | 2 |
| #23749622 | 2 |
| C2×#18011836 | 2 |
| #405×C149 | 2 |
| #3137 | 149 |