Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1250 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 344 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. #22625668 | C2 | semidirect |
| 3. C22⋊C4×#10596833 | C2 | semidirect |
| 4. #22625661 | C2 | semidirect |
| 7. C2×C22⋊#10596833 | C4 | semidirect |
| 11. C2×#14556646 | C22 | semidirect |
| 12. C2×C4×#10596833 | C22 | semidirect |
| 13. #17989453 | C22 | semidirect |
| 132. C73 | #20528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10596833 | 2 |
| #22625668 | 2 |
| C22⋊C4×#10596833 | 2 |
| #22625661 | 2 |
| #22612309 | 2 |
| #20528 | 73 |