Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #23749990 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749980 | C2 | semidirect |
| 6. #23749972 | C2 | semidirect |
| 7. #23749631 | C2 | semidirect |
| 8. #23749627 | C2 | semidirect |
| 9. #23749622 | C2 | semidirect |
| 10. C2×#18011833 | C2 | semidirect |
| 11. #405×C149 | C2 | semidirect |
| 14. #18011911 | C22 | semidirect |
| 17. #18011903 | C22 | semidirect |
| 26. #18011836 | C22 | semidirect |
| 27. #18011836 | C22 | semidirect |
| 28. #18011836 | C22 | semidirect |
| 33. #18011833 | C22 | semidirect |
| 34. #18011833 | C22 | semidirect |
| 35. #18011833 | C22 | semidirect |
| 39. #97×C149 | C22 | semidirect |
| 40. C4×C8×C149 | C22 | semidirect |
| 135. C149 | #3136 | semidirect |
| 147. #405 | D149 | semidirect |
| 175. #97 | C2×D149 | semidirect |
| 176. C4×C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750253 | 2 |
| #23750194 | 2 |
| #23749990 | 2 |
| #23749985 | 2 |
| #23749980 | 2 |
| #23749972 | 2 |
| #23749631 | 2 |
| #23749627 | 2 |
| #23749622 | 2 |
| C2×#18011833 | 2 |
| #405×C149 | 2 |
| #3136 | 149 |