Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22561981 | C2 | semidirect |
| 3. C2×#16863210 | C2 | semidirect |
| 4. #22561924 | C2 | semidirect |
| 5. #22561838 | C2 | semidirect |
| 6. #22560260 | C2 | semidirect |
| 7. C67×#1384 | C2 | semidirect |
| 47. C2×C67⋊C16 | D4 | semidirect |
| 172. #1384 | D67 | semidirect |
| 173. C67 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569858 | 2 |
| #22561981 | 2 |
| C2×#16863210 | 2 |
| #22561924 | 2 |
| #22561838 | 2 |
| #22560260 | 2 |
| C67×#1384 | 2 |
| #13396 | 67 |