Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
328 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 328 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 |
|---|---|---|
| 1. #22612188 | C2 | semidirect |
| 3. #22609291 | C2 | semidirect |
| 4. #22607980 | C2 | semidirect |
| 5. Q8⋊#11924003 | C2 | semidirect |
| 6. #22607892 | C2 | semidirect |
| 7. C73×#3393 | C2 | semidirect |
| 138. #3393 | 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 |
|---|---|
| #22612188 | 2 |
| #22611966 | 2 |
| #22609291 | 2 |
| #22607980 | 2 |
| Q8⋊#11924003 | 2 |
| #22607892 | 2 |
| C73×#3393 | 2 |
| #12331 | 73 |