Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
774 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 166 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. #22625864 | C2 | semidirect |
| 2. C42×#10596833 | C2 | semidirect |
| 3. C2×#17989435 | C2 | semidirect |
| 4. C2×D4⋊#10596833 | C2 | semidirect |
| 28. C4×#10596833 | D4 | semidirect |
| 34. #14556587 | C8 | semidirect |
| 166. Dic73 | D4⋊C8 | semidirect |
| 183. C73 | #9638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625864 | 2 |
| C42×#10596833 | 2 |
| C2×#17989435 | 2 |
| C2×D4⋊#10596833 | 2 |
| #22612495 | 2 |
| #9638 | 73 |