Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22626932 | C2 | semidirect |
| 42. C22×Dic146 | C8 | semidirect |
| 47. C2×Q8×D73 | C8 | semidirect |
| 51. C22×Q8×C73 | C8 | semidirect |
| 208. C73 | #7575 | semidirect |
| 232. 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 |
| #22626932 | 2 |
| C2×(C2×#64408)⋊Q8 | 2 |
| #7575 | 73 |