Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 92 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×#17989518 | C2 | semidirect |
| 2. C22×#14556641 | C2 | semidirect |
| 3. #22625089 | C2 | semidirect |
| 4. #22625045 | C2 | semidirect |
| 5. C22⋊#14556641 | C2 | semidirect |
| 6. #22625036 | C2 | semidirect |
| 24. #14556641 | D4 | semidirect |
| 66. C22⋊D73 | C32 | semidirect |
| 79. C22×C73 | C2×C32 | semidirect |
| 83. C2×D73 | C2×C32 | semidirect |
| 89. Dic73 | C2×C32 | semidirect |
| 103. C73 | D4×C32 | semidirect |
| 178. C22 | #17989518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| C22×#14556641 | 2 |
| #22625089 | 2 |
| #22625045 | 2 |
| C22⋊#14556641 | 2 |
| #22625036 | 2 |
| #22611748 | 2 |
| D4×C32 | 73 |