Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4⋊C16×D67 | C2 | semidirect |
| 3. #22558966 | C2 | semidirect |
| 4. #22558264 | C2 | semidirect |
| 5. #22558256 | C2 | semidirect |
| 6. #22558254 | C2 | semidirect |
| 7. C67×#1364 | C2 | semidirect |
| 143. #1364 | D67 | semidirect |
| 146. C67 | #11981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570789 | 2 |
| C4⋊C16×D67 | 2 |
| #22558966 | 2 |
| #22558264 | 2 |
| #22558256 | 2 |
| #22558254 | 2 |
| C67×#1364 | 2 |
| #11981 | 67 |