Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1088 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×Q8⋊#10596842 | C2 | semidirect |
| 52. C22×Dic146 | C8 | semidirect |
| 57. C2×Q8×D73 | C8 | semidirect |
| 61. C22×Q8×C73 | C8 | semidirect |
| 160. Q8×C73 | C22⋊C8 | semidirect |
| 185. Dic146 | C22⋊C8 | semidirect |
| 188. C22×C73 | Q8⋊C8 | semidirect |
| 196. C2×D73 | Q8⋊C8 | semidirect |
| 229. C73 | #8311 | semidirect |
| 255. C22×Q8 | #10596842 | semidirect |
| 369. Q8 | C22⋊#10596842 | semidirect |
| 426. C22 | Q8⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C4×C22⋊#10596842 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C22×Q8×#64408 | 2 |
| #8311 | 73 |