Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 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. #22561995 | C2 | semidirect |
| 3. C2×#16863206 | C2 | semidirect |
| 4. C2×#16863177 | C2 | semidirect |
| 5. #22560243 | C2 | semidirect |
| 6. #22558315 | C2 | semidirect |
| 7. C67×#2139 | C2 | semidirect |
| 49. #14523983 | D4 | semidirect |
| 211. #2139 | D67 | semidirect |
| 215. C67 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569814 | 2 |
| #22561995 | 2 |
| C2×#16863206 | 2 |
| C2×#16863177 | 2 |
| #22560243 | 2 |
| #22558315 | 2 |
| C67×#2139 | 2 |
| #13386 | 67 |