Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #22627055 | C2 | semidirect |
| 3. #22626935 | C2 | semidirect |
| 44. C2×#11924012 | C8 | semidirect |
| 45. C2×#11924011 | C8 | semidirect |
| 46. C2×#11924011 | C8 | semidirect |
| 51. C2×M16×C73 | C8 | semidirect |
| 174. C73 | #8602 | semidirect |
| 195. C2×M16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22627043 | 2 |
| #22626935 | 2 |
| C2×#17989553 | 2 |
| #8602 | 73 |