Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 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. #23749581 | C2 | semidirect |
| 5. C2×C4×#11924746 | C2 | semidirect |
| 6. #23749389 | C2 | semidirect |
| 7. #339×C149 | C2 | semidirect |
| 10. #18011919 | C4 | semidirect |
| 16. #18011839 | C4 | semidirect |
| 17. #18011834 | C4 | semidirect |
| 18. #18011831 | C4 | semidirect |
| 98. C149 | #1764 | semidirect |
| 106. #339 | 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×#18011839 | 2 |
| #23749619 | 2 |
| #23749581 | 2 |
| C2×C4×#11924746 | 2 |
| #23749389 | 2 |
| #339×C149 | 2 |
| #1764 | 149 |