Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 2. #23749917 | C2 | semidirect |
| 3. #23749912 | C2 | semidirect |
| 4. #23749907 | C2 | semidirect |
| 5. #23749902 | C2 | semidirect |
| 6. #23749665 | C2 | semidirect |
| 7. #23749649 | C2 | semidirect |
| 9. C2×C4⋊Q8×C149 | C2 | semidirect |
| 36. #14558736 | Q8 | semidirect |
| 72. Dic298 | C2×Q8 | semidirect |
| 74. D596 | C2×Q8 | semidirect |
| 121. C149 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14558736 | 2 |
| #23749917 | 2 |
| #23749912 | 2 |
| #23749907 | 2 |
| #23749902 | 2 |
| #23749665 | 2 |
| #23749649 | 2 |
| #23749624 | 2 |
| C2×C4⋊Q8×C149 | 2 |
| #3079 | 149 |