Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
316 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562482 | C2 | semidirect |
| 3. #22559600 | C2 | semidirect |
| 4. #22558263 | C2 | semidirect |
| 5. #22558187 | C2 | semidirect |
| 73. D8×C67 | Q16 | semidirect |
| 134. C67 | #12404 | semidirect |
| 190. D8 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic134 | 2 |
| #22562482 | 2 |
| #22559600 | 2 |
| #22558263 | 2 |
| #22558187 | 2 |
| #22558170 | 2 |
| C67×#2224 | 2 |
| #12404 | 67 |