Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. C2×#18011918 | C2 | semidirect |
| 3. #23749633 | C2 | semidirect |
| 4. #23749624 | C2 | semidirect |
| 5. #23749619 | C2 | semidirect |
| 6. C2×#18011834 | C2 | semidirect |
| 7. #520×C149 | C2 | semidirect |
| 9. #18011958 | C4 | semidirect |
| 28. #14558736 | C2×C4 | semidirect |
| 32. C2×Dic298 | C2×C4 | semidirect |
| 94. C149 | #2898 | semidirect |
| 98. #520 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011958 | 2 |
| C2×#18011918 | 2 |
| #23749633 | 2 |
| #23749624 | 2 |
| #23749619 | 2 |
| C2×#18011834 | 2 |
| #520×C149 | 2 |
| #2898 | 149 |