Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22611848 | C2 | semidirect |
| 3. #22611050 | C2 | semidirect |
| 4. #22607947 | C2 | semidirect |
| 5. #22607946 | C2 | semidirect |
| 6. #22607856 | C2 | semidirect |
| 7. C73×#2185 | C2 | semidirect |
| 20. C22⋊#11924003 | C22 | semidirect |
| 21. #17988352 | C22 | semidirect |
| 22. C22×Q16×C73 | C22 | semidirect |
| 26. C22⋊C16×C73 | C22 | semidirect |
| 187. #2185 | D73 | semidirect |
| 192. C73 | #12111 | semidirect |
| 194. C22×Q16 | C2×D73 | semidirect |
| 210. C22⋊C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620791 | 2 |
| #22611848 | 2 |
| #22611050 | 2 |
| #22607947 | 2 |
| #22607946 | 2 |
| #22607856 | 2 |
| C73×#2185 | 2 |
| #12111 | 73 |