Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×#17984095 | C2 | semidirect |
| 2. #22577404 | C2 | semidirect |
| 3. C2×#17984009 | C2 | semidirect |
| 4. C2×#17984005 | C2 | semidirect |
| 5. #22577171 | C2 | semidirect |
| 6. #22577167 | C2 | semidirect |
| 24. AGL(1,ℤ/8)×C137 | C4 | semidirect |
| 123. C137 | #1907 | semidirect |
| 135. AGL(1,ℤ/8) | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984095 | 2 |
| #22577404 | 2 |
| C2×#17984009 | 2 |
| C2×#17984005 | 2 |
| #22577171 | 2 |
| #22577167 | 2 |
| C2×AGL(1,ℤ/8)×C137 | 2 |
| #1907 | 137 |