Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#18011909 | C2 | semidirect |
| 3. #23750018 | C2 | semidirect |
| 4. #23749992 | C2 | semidirect |
| 5. #23749833 | C2 | semidirect |
| 6. #23749829 | C2 | semidirect |
| 7. #23749780 | C2 | semidirect |
| 10. #23749679 | C2 | semidirect |
| 11. #451×C149 | C2 | semidirect |
| 137. C149 | #3218 | semidirect |
| 146. #451 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011909 | 2 |
| #23750161 | 2 |
| #23750018 | 2 |
| #23749992 | 2 |
| #23749833 | 2 |
| #23749829 | 2 |
| #23749780 | 2 |
| #23749766 | 2 |
| #23749764 | 2 |
| #23749679 | 2 |
| #451×C149 | 2 |
| #3218 | 149 |