Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#16863213 | C2 | semidirect |
| 4. #22561930 | C2 | semidirect |
| 6. #22560957 | C2 | semidirect |
| 7. C67×#1376 | C2 | semidirect |
| 166. #1376 | D67 | semidirect |
| 167. C67 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863780 | 2 |
| C2×#16863213 | 2 |
| C2×#16863210 | 2 |
| #22561930 | 2 |
| #22561926 | 2 |
| #22560957 | 2 |
| C67×#1376 | 2 |
| #13414 | 67 |