Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1050 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 30. C22×Dic146 | C8 | semidirect |
| 31. C22×Dic146 | C8 | semidirect |
| 38. C22×Q8×C73 | C8 | semidirect |
| 149. C73 | #8303 | semidirect |
| 166. C22×Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627072 | 2 |
| C2×#17989673 | 2 |
| C22×Q8×#64408 | 2 |
| #8303 | 73 |