Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
184 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22578506 | C2 | direct (N × H) |
| 27. C2×Dic137 | C16 | semidirect |
| 42. Dic137 | C2×C16 | semidirect |
| 45. C2×C137 | C4⋊C16 | semidirect |
| 49. C137 | C2×C4⋊C16 | semidirect |
| 95. C2 | #22578506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555522 | 2 |
| #22578506 | 2 |
| C2×C4×#11764047 | 2 |
| C2×C4⋊C16 | 137 |