Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
328 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22622920 | C2 | semidirect |
| 2. #22612187 | C2 | semidirect |
| 4. #22609291 | C2 | semidirect |
| 5. #22607981 | C2 | semidirect |
| 6. #22607893 | C2 | semidirect |
| 7. C73×Q8⋊C16 | C2 | semidirect |
| 143. Q8⋊C16 | D73 | semidirect |
| 145. C73 | #12331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622920 | 2 |
| #22612187 | 2 |
| #22611967 | 2 |
| #22609291 | 2 |
| #22607981 | 2 |
| #22607893 | 2 |
| C73×Q8⋊C16 | 2 |
| #12331 | 73 |