Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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. #22578267 | C2 | semidirect |
| 4. #22578266 | C2 | semidirect |
| 5. #22578265 | C2 | semidirect |
| 6. #22578264 | C2 | semidirect |
| 53. #11764040 | M16 | semidirect |
| 60. C8×C137 | M16 | semidirect |
| 77. C137 | #1569 | semidirect |
| 138. C8 | #14555519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578424 | 2 |
| #22578406 | 2 |
| #22578267 | 2 |
| #22578266 | 2 |
| #22578265 | 2 |
| #22578264 | 2 |
| M16×Dic137 | 2 |
| #1569 | 137 |