Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 3. #23750019 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749848 | C2 | semidirect |
| 6. #23749783 | C2 | semidirect |
| 8. #432×C149 | C2 | semidirect |
| 11. C2×Dic596 | C22 | semidirect |
| 13. #18011911 | C22 | semidirect |
| 14. #18011911 | C22 | semidirect |
| 23. C4×Dic298 | C22 | semidirect |
| 27. #18011836 | C22 | semidirect |
| 30. C4⋊C8×C149 | C22 | semidirect |
| 32. #97×C149 | C22 | semidirect |
| 112. C149 | #3215 | semidirect |
| 121. #432 | D149 | semidirect |
| 141. C4⋊C8 | C2×D149 | semidirect |
| 145. #97 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| C2×#18011899 | 2 |
| #23750019 | 2 |
| #23749985 | 2 |
| #23749848 | 2 |
| #23749783 | 2 |
| #23749778 | 2 |
| #432×C149 | 2 |
| #3215 | 149 |