Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#18011958 | C2 | semidirect |
| 2. C2×#18011944 | C2 | semidirect |
| 3. C2×#18011931 | C2 | semidirect |
| 4. #23750206 | C2 | semidirect |
| 5. #23749788 | C2 | semidirect |
| 6. #23749782 | C2 | semidirect |
| 7. #23749771 | C2 | semidirect |
| 8. #23749765 | C2 | semidirect |
| 9. C2×#18011834 | C2 | semidirect |
| 10. #23749593 | C2 | semidirect |
| 11. #417×C149 | C2 | semidirect |
| 58. C2×Dic298 | D4 | semidirect |
| 87. #41×C149 | D4 | semidirect |
| 169. C149 | #3013 | semidirect |
| 179. #417 | D149 | semidirect |
| 224. #41 | D596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011958 | 2 |
| C2×#18011944 | 2 |
| C2×#18011931 | 2 |
| #23750206 | 2 |
| #23749788 | 2 |
| #23749782 | 2 |
| #23749771 | 2 |
| #23749765 | 2 |
| C2×#18011834 | 2 |
| #23749593 | 2 |
| #417×C149 | 2 |
| #3013 | 149 |