Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#17989514 | C2 | semidirect |
| 4. #22624989 | C2 | semidirect |
| 17. C22⋊#11924003 | C4 | semidirect |
| 18. #17988366 | C4 | semidirect |
| 19. C22⋊C16×C73 | C4 | semidirect |
| 42. C2×#11924003 | C2×C4 | semidirect |
| 46. C2×C16×C73 | C2×C4 | semidirect |
| 129. C22×C73 | #367 | semidirect |
| 137. C2×D73 | #367 | semidirect |
| 168. C73 | #12920 | semidirect |
| 181. C22⋊C16 | #64408 | semidirect |
| 203. C2×C16 | C2×#64408 | semidirect |
| 305. C22 | #17989514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556660 | 2 |
| C2×#17989514 | 2 |
| #22625808 | 2 |
| #22624989 | 2 |
| C22⋊C16×D73 | 2 |
| #12920 | 73 |