Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16863205 | C2 | semidirect |
| 4. #22561919 | C2 | semidirect |
| 5. C2×#16863178 | C2 | semidirect |
| 6. #22558316 | C2 | semidirect |
| 7. C67×#1809 | C2 | semidirect |
| 49. #14523983 | D4 | semidirect |
| 213. #1809 | 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 |
|---|---|
| #22569818 | 2 |
| #22561995 | 2 |
| C2×#16863205 | 2 |
| #22561919 | 2 |
| C2×#16863178 | 2 |
| #22558316 | 2 |
| C67×#1809 | 2 |
| #13386 | 67 |