Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
432 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 110 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. C23×#11764047 | C2 | semidirect |
| 2. C2×#17984145 | C2 | semidirect |
| 3. C2×C22⋊#11764047 | C2 | semidirect |
| 4. #22578269 | C2 | semidirect |
| 27. C2×#11764047 | D4 | semidirect |
| 31. C2×C22⋊D137 | C8 | semidirect |
| 57. C22×D137 | C2×C8 | semidirect |
| 66. C2×Dic137 | C2×C8 | semidirect |
| 88. C22×C137 | C22⋊C8 | semidirect |
| 113. C137 | #1869 | semidirect |
| 207. C22 | #17984145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11764047 | 2 |
| C2×#17984145 | 2 |
| C2×C22⋊#11764047 | 2 |
| #22578269 | 2 |
| C2×#17984048 | 2 |
| #1869 | 137 |