Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
502 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 43. C2×Dic292 | C8 | semidirect |
| 44. C2×#11924018 | C8 | semidirect |
| 48. C2×Q16×C73 | C8 | semidirect |
| 55. C2×#10596842 | Q16 | semidirect |
| 148. C73 | #9656 | semidirect |
| 168. C2×Q16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10596842)⋊Q8 | 2 |
| C2×#17989677 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C2×C8×#10596842 | 2 |
| C2×Q16×#64408 | 2 |
| #9656 | 73 |