Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
204 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 100 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. C2×#17989519 | C2 | semidirect |
| 2. C22×#14556641 | C2 | semidirect |
| 3. C4⋊#14556641 | C2 | semidirect |
| 4. C22⋊#14556641 | C2 | semidirect |
| 5. C22⋊#14556641 | C2 | semidirect |
| 6. #22625038 | C2 | semidirect |
| 24. #14556641 | D4 | semidirect |
| 82. C22×C73 | M64 | semidirect |
| 103. C73 | #13645 | semidirect |
| 178. C22 | #17989519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989519 | 2 |
| C22×#14556641 | 2 |
| C4⋊#14556641 | 2 |
| C22⋊#14556641 | 2 |
| #22625038 | 2 |
| D4×#11924003 | 2 |
| #13645 | 73 |