Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
174 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#17984161 | C2 | semidirect |
| 2. C4⋊#14555513 | C2 | semidirect |
| 3. #22578298 | C2 | semidirect |
| 4. C4×#14555513 | C2 | semidirect |
| 17. #14555513 | D4 | semidirect |
| 29. D548 | C16 | semidirect |
| 43. C2×D137 | C2×C16 | semidirect |
| 45. C4×C137 | C2×C16 | semidirect |
| 53. C137 | D4×C16 | semidirect |
| 100. C4 | #17984161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| C4⋊#14555513 | 2 |
| #22578298 | 2 |
| C4×#14555513 | 2 |
| #22577468 | 2 |
| D4×C16 | 137 |