Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
446 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 51. C2×Dic292 | C8 | semidirect |
| 52. C2×#11924018 | C8 | semidirect |
| 58. C2×Q16×C73 | C8 | semidirect |
| 161. C73 | #9669 | semidirect |
| 187. C2×Q16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22627052 | 2 |
| #22627046 | 2 |
| #22627040 | 2 |
| C2×Q16×#64408 | 2 |
| #9669 | 73 |