Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 47. C4×Dic137 | Q8 | semidirect |
| 55. C42×C137 | Q8 | semidirect |
| 102. C137 | #2399 | semidirect |
| 158. C42 | Dic274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic274 | 2 |
| #22577337 | 2 |
| #22577336 | 2 |
| #22577324 | 2 |
| #22577323 | 2 |
| C4×#14555489 | 2 |
| C4×C4⋊Dic137 | 2 |
| #22577249 | 2 |
| C4×C4⋊C4×C137 | 2 |
| #2399 | 137 |