Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
356 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22612159 | C2 | semidirect |
| 3. #22612069 | C2 | semidirect |
| 4. #22609320 | C2 | semidirect |
| 5. #22607981 | C2 | semidirect |
| 6. #22607893 | C2 | semidirect |
| 7. C73×D4⋊C16 | C2 | semidirect |
| 68. D584 | SD16 | semidirect |
| 146. D4⋊C16 | D73 | semidirect |
| 147. C73 | #12371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621653 | 2 |
| #22612159 | 2 |
| #22612069 | 2 |
| #22609320 | 2 |
| #22607981 | 2 |
| #22607893 | 2 |
| C73×D4⋊C16 | 2 |
| #12371 | 73 |