Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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. #23750182 | C2 | semidirect |
| 2. #23749984 | C2 | semidirect |
| 3. #23749979 | C2 | semidirect |
| 4. #23749634 | C2 | semidirect |
| 6. C4×#14558720 | C2 | semidirect |
| 9. #18011911 | C22 | semidirect |
| 10. #18011903 | C22 | semidirect |
| 14. #18011835 | C22 | semidirect |
| 16. #18011822 | C22 | semidirect |
| 17. C4×#11924746 | C22 | semidirect |
| 83. C149 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| #23749984 | 2 |
| #23749979 | 2 |
| #23749634 | 2 |
| #23749630 | 2 |
| C4×#14558720 | 2 |
| C2×#124×C149 | 2 |
| #3140 | 149 |