Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #23749583 | C2 | semidirect |
| 5. C2×#18011821 | C2 | semidirect |
| 6. #23749386 | C2 | semidirect |
| 7. #341×C149 | C2 | semidirect |
| 10. #18011919 | C4 | semidirect |
| 16. #18011837 | C4 | semidirect |
| 17. #18011836 | C4 | semidirect |
| 18. #18011833 | C4 | semidirect |
| 98. C149 | #1765 | semidirect |
| 105. #341 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011919 | 2 |
| C2×#18011837 | 2 |
| #23749622 | 2 |
| #23749583 | 2 |
| C2×#18011821 | 2 |
| #23749386 | 2 |
| #341×C149 | 2 |
| #1765 | 149 |