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 |
| 2. #23749993 | C2 | semidirect |
| 3. #23749984 | C2 | semidirect |
| 4. #23749979 | C2 | semidirect |
| 5. #23749975 | C2 | semidirect |
| 6. #23749634 | C2 | semidirect |
| 9. C2×#18011835 | C2 | semidirect |
| 10. #23749581 | C2 | semidirect |
| 127. C149 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750253 | 2 |
| #23749993 | 2 |
| #23749984 | 2 |
| #23749979 | 2 |
| #23749975 | 2 |
| #23749634 | 2 |
| #23749626 | 2 |
| #23749621 | 2 |
| C2×#18011835 | 2 |
| #23749581 | 2 |
| #536×C149 | 2 |
| #3137 | 149 |