Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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. #22578452 | C2 | semidirect |
| 3. #22578265 | C2 | semidirect |
| 4. #22578253 | C2 | semidirect |
| 6. C8×#11764047 | C2 | semidirect |
| 31. #14555498 | C8 | semidirect |
| 45. #11764047 | SD16 | semidirect |
| 47. Dic274 | C2×C8 | semidirect |
| 54. #11764040 | C2×C8 | semidirect |
| 77. C137 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578452 | 2 |
| D4×#11764047 | 2 |
| #22578265 | 2 |
| #22578253 | 2 |
| D4⋊#11764047 | 2 |
| C8×#11764047 | 2 |
| #22577494 | 2 |
| C8×SD16 | 137 |