Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22627081 | C2 | semidirect |
| 2. C2×#17989676 | C2 | semidirect |
| 3. C2×D4⋊#10596842 | C2 | semidirect |
| 4. C2×#17989671 | C2 | semidirect |
| 44. C2×D584 | C8 | semidirect |
| 45. C2×#11924013 | C8 | semidirect |
| 49. C2×D8×C73 | C8 | semidirect |
| 124. C8×C73 | C22⋊C8 | semidirect |
| 125. #10596831 | C22⋊C8 | semidirect |
| 160. C73 | #9659 | semidirect |
| 181. C2×D8 | #10596842 | semidirect |
| 280. C8 | C22⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627081 | 2 |
| C2×#17989676 | 2 |
| C2×D4⋊#10596842 | 2 |
| C2×#17989671 | 2 |
| C2×D8×#64408 | 2 |
| #9659 | 73 |