Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
368 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612183 | C2 | semidirect |
| 4. #22607981 | C2 | semidirect |
| 5. #22607895 | C2 | semidirect |
| 7. C73×#2209 | C2 | semidirect |
| 108. D292 | Q32 | semidirect |
| 141. #2209 | D73 | semidirect |
| 146. C73 | #12322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D292 | 2 |
| #22612183 | 2 |
| #22609293 | 2 |
| #22607981 | 2 |
| #22607895 | 2 |
| #22607885 | 2 |
| C73×#2209 | 2 |
| #12322 | 73 |