Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
312 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22612156 | C2 | semidirect |
| 3. #22609291 | C2 | semidirect |
| 4. #22607989 | C2 | semidirect |
| 5. Q8⋊#11924003 | C2 | semidirect |
| 6. #22607892 | C2 | semidirect |
| 7. C73×#3380 | C2 | semidirect |
| 69. D8×C73 | SD16 | semidirect |
| 133. #3380 | D73 | semidirect |
| 140. C73 | #12355 | semidirect |
| 199. D8 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612156 | 2 |
| #22611966 | 2 |
| #22609291 | 2 |
| #22607989 | 2 |
| Q8⋊#11924003 | 2 |
| #22607892 | 2 |
| C73×#3380 | 2 |
| #12355 | 73 |