Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 382 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. #22562003 | C2 | semidirect |
| 3. C2×#16863213 | C2 | semidirect |
| 4. C2×#16863211 | C2 | semidirect |
| 7. C67×#1388 | C2 | semidirect |
| 165. #1388 | D67 | semidirect |
| 166. C67 | #13390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863672 | 2 |
| #22562003 | 2 |
| C2×#16863213 | 2 |
| C2×#16863211 | 2 |
| #22561836 | 2 |
| #22560256 | 2 |
| C67×#1388 | 2 |
| #13390 | 67 |