Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
480 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 2. #22578269 | C2 | semidirect |
| 6. C2×#14555519 | C4 | semidirect |
| 17. C2×#11764047 | C2×C4 | semidirect |
| 42. C2×Dic137 | M16 | semidirect |
| 56. C2×C4×C137 | M16 | semidirect |
| 78. C137 | #1728 | semidirect |
| 134. C2×C4 | #14555519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555519 | 2 |
| #22578269 | 2 |
| C22×C4×Dic137 | 2 |
| #1728 | 137 |