Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22578245 | C2 | semidirect |
| 4. #22578244 | C2 | semidirect |
| 44. #11764040 | M16 | semidirect |
| 51. C8×C137 | M16 | semidirect |
| 67. C137 | #1451 | semidirect |
| 119. C8 | #14555519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578420 | 2 |
| C4×#14555519 | 2 |
| #22578245 | 2 |
| #22578244 | 2 |
| C2×C8×Dic137 | 2 |
| #1451 | 137 |