Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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. #23750180 | C2 | semidirect |
| 3. #23749962 | C2 | semidirect |
| 4. #23749902 | C2 | semidirect |
| 5. #23749831 | C2 | semidirect |
| 6. #23749830 | C2 | semidirect |
| 8. #23749724 | C2 | semidirect |
| 9. #23749722 | C2 | semidirect |
| 10. #23749681 | C2 | semidirect |
| 11. #474×C149 | C2 | semidirect |
| 16. #18011911 | C22 | semidirect |
| 21. #18011876 | C22 | semidirect |
| 31. #18011844 | C22 | semidirect |
| 32. C4⋊#11924746 | C22 | semidirect |
| 33. #18011836 | C22 | semidirect |
| 34. #18011834 | C22 | semidirect |
| 37. #18011821 | C22 | semidirect |
| 38. C4⋊Q8×C149 | C22 | semidirect |
| 40. #107×C149 | C22 | semidirect |
| 41. C4⋊C8×C149 | C22 | semidirect |
| 146. C149 | #3110 | semidirect |
| 152. #474 | D149 | semidirect |
| 164. C4⋊Q8 | C2×D149 | semidirect |
| 181. #107 | C2×D149 | semidirect |
| 183. C4⋊C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| C4×D4×D149 | 2 |
| #23749962 | 2 |
| #23749902 | 2 |
| #23749831 | 2 |
| #23749830 | 2 |
| #23749777 | 2 |
| #23749724 | 2 |
| #23749722 | 2 |
| #23749681 | 2 |
| #474×C149 | 2 |
| #3110 | 149 |