Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
314 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 4. C22×#11924031 | C4 | semidirect |
| 13. C22⋊#11924003 | C4 | semidirect |
| 15. C22⋊C16×C73 | C4 | semidirect |
| 41. C22⋊#64408 | C16 | semidirect |
| 124. C73 | #7199 | semidirect |
| 135. C22⋊C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989482 | 2 |
| C8×C22⋊#64408 | 2 |
| C22⋊C16×D73 | 2 |
| #7199 | 73 |