Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #22610916 | C2 | semidirect |
| 4. #22608465 | C2 | semidirect |
| 5. #22607836 | C2 | semidirect |
| 6. #22607784 | C2 | semidirect |
| 10. #17988898 | C4 | semidirect |
| 13. #17988725 | C4 | semidirect |
| 31. C22×Dic146 | C2×C4 | semidirect |
| 41. C2×C4⋊Dic73 | C2×C4 | semidirect |
| 55. C22⋊#10596831 | C2×C4 | semidirect |
| 237. C73 | #9341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620737 | 2 |
| #22613088 | 2 |
| #22610916 | 2 |
| #22608465 | 2 |
| #22607836 | 2 |
| #22607784 | 2 |
| C73×#1507 | 2 |
| #9341 | 73 |