Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
460 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 3. #22578418 | C2 | direct (N × H) |
| 4. C2×#17984159 | C2 | semidirect |
| 5. C2×#17984158 | C2 | semidirect |
| 18. #17984159 | C22 | semidirect |
| 19. #17984158 | C22 | semidirect |
| 104. C2×C137 | #430 | semidirect |
| 109. C137 | C2×#430 | semidirect |
| 217. C2 | #22578418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555520 | 2 |
| C2×D137⋊M16 | 2 |
| #22578418 | 2 |
| C2×#17984159 | 2 |
| C2×#17984158 | 2 |
| C2×M16×D137 | 2 |
| C2×#430 | 137 |