Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23749992 | C2 | semidirect |
| 4. #23749986 | C2 | semidirect |
| 5. #23749981 | C2 | semidirect |
| 6. #23749974 | C2 | semidirect |
| 9. C2×#18011835 | C2 | semidirect |
| 10. #23749583 | C2 | semidirect |
| 11. #419×C149 | C2 | semidirect |
| 127. C149 | #3137 | semidirect |
| 135. #419 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750253 | 2 |
| #23750199 | 2 |
| #23749992 | 2 |
| #23749986 | 2 |
| #23749981 | 2 |
| #23749974 | 2 |
| #23749627 | 2 |
| #23749619 | 2 |
| C2×#18011835 | 2 |
| #23749583 | 2 |
| #419×C149 | 2 |
| #3137 | 149 |