Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #22577788 | C2 | semidirect |
| 3. D8×Dic137 | C2 | semidirect |
| 4. #22577221 | C2 | semidirect |
| 5. #22577207 | C2 | semidirect |
| 6. #22577205 | C2 | semidirect |
| 7. C2×SD32×C137 | C2 | semidirect |
| 76. C137 | #2210 | semidirect |
| 78. C2×SD32 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984029 | 2 |
| #22577788 | 2 |
| D8×Dic137 | 2 |
| #22577221 | 2 |
| #22577207 | 2 |
| #22577205 | 2 |
| C2×SD32×C137 | 2 |
| #2210 | 137 |