Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750256 | C2 | semidirect |
| 3. #23749988 | C2 | semidirect |
| 4. #23749983 | C2 | semidirect |
| 5. #23749978 | C2 | semidirect |
| 6. #23749970 | C2 | semidirect |
| 7. #23749630 | C2 | semidirect |
| 8. #23749624 | C2 | semidirect |
| 9. #23749622 | C2 | semidirect |
| 10. #23749580 | C2 | semidirect |
| 11. C2×#102×C149 | C2 | semidirect |
| 15. #18011910 | C22 | semidirect |
| 18. #18011902 | C22 | semidirect |
| 26. #18011836 | C22 | semidirect |
| 27. #18011836 | C22 | semidirect |
| 28. #18011834 | C22 | semidirect |
| 29. #18011833 | C22 | semidirect |
| 30. #18011833 | C22 | semidirect |
| 33. #18011831 | C22 | semidirect |
| 34. #18011821 | C22 | semidirect |
| 35. C8×Dic149 | C22 | semidirect |
| 135. C149 | #3136 | semidirect |
| 146. C2×#102 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750256 | 2 |
| #23750192 | 2 |
| #23749988 | 2 |
| #23749983 | 2 |
| #23749978 | 2 |
| #23749970 | 2 |
| #23749630 | 2 |
| #23749624 | 2 |
| #23749622 | 2 |
| #23749580 | 2 |
| C2×#102×C149 | 2 |
| #3136 | 149 |