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×#18011959 | C2 | semidirect |
| 2. C2×#18011931 | C2 | semidirect |
| 3. #23750203 | C2 | semidirect |
| 4. #23749786 | C2 | semidirect |
| 5. #23749779 | C2 | semidirect |
| 6. #23749769 | C2 | semidirect |
| 7. #23749762 | C2 | semidirect |
| 8. #23749627 | C2 | semidirect |
| 9. C2×#18011835 | C2 | semidirect |
| 10. #23749593 | C2 | semidirect |
| 11. C2×#137×C149 | C2 | semidirect |
| 52. #14558736 | D4 | semidirect |
| 86. C2×Q8×C149 | D4 | semidirect |
| 169. C149 | #3013 | semidirect |
| 172. C2×#137 | D149 | semidirect |
| 233. C2×Q8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011959 | 2 |
| C2×#18011931 | 2 |
| #23750203 | 2 |
| #23749786 | 2 |
| #23749779 | 2 |
| #23749769 | 2 |
| #23749762 | 2 |
| #23749627 | 2 |
| C2×#18011835 | 2 |
| #23749593 | 2 |
| C2×#137×C149 | 2 |
| #3013 | 149 |