Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
196 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22578497 | C2 | semidirect |
| 3. C4×#14555522 | C2 | semidirect |
| 5. #17984184 | C4 | direct (N × H) |
| 14. #14555522 | C2×C4 | semidirect |
| 48. C4×C137 | M32 | semidirect |
| 51. Dic137 | M32 | semidirect |
| 58. C137 | C4×M32 | semidirect |
| 112. C4 | #17984184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984184 | 2 |
| #22578497 | 2 |
| C4×#14555522 | 2 |
| C2×C4×#11764047 | 2 |
| C4×M32 | 137 |