Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #22578328 | C2 | semidirect |
| 4. #22578327 | C2 | semidirect |
| 14. #17984028 | C4 | semidirect |
| 16. C16×D137 | C4 | semidirect |
| 17. M32×C137 | C4 | semidirect |
| 31. #14555485 | C2×C4 | semidirect |
| 33. C16×C137 | C2×C4 | semidirect |
| 61. D137 | #365 | semidirect |
| 62. C137 | C2×#365 | semidirect |
| 74. M32 | #10587739 | semidirect |
| 96. C16 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#108 | 2 |
| C2×#17984156 | 2 |
| #22578328 | 2 |
| #22578327 | 2 |
| M32×D137 | 2 |
| C2×#365 | 137 |