Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011944 | C2 | semidirect |
| 3. C22×#14558726 | C2 | semidirect |
| 4. #23750199 | C2 | semidirect |
| 5. #23750196 | C2 | semidirect |
| 6. #23750018 | C2 | semidirect |
| 7. #23750016 | C2 | semidirect |
| 8. #23750006 | C2 | semidirect |
| 9. #23750003 | C2 | semidirect |
| 10. #23749583 | C2 | semidirect |
| 11. C2×#137×C149 | C2 | semidirect |
| 143. C149 | #3156 | semidirect |
| 146. C2×#137 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011944 | 2 |
| C2×#18011931 | 2 |
| C22×#14558726 | 2 |
| #23750199 | 2 |
| #23750196 | 2 |
| #23750018 | 2 |
| #23750016 | 2 |
| #23750006 | 2 |
| #23750003 | 2 |
| #23749583 | 2 |
| C2×#137×C149 | 2 |
| #3156 | 149 |