Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 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×#16863210 | C2 | semidirect |
| 3. C2×#16863204 | C2 | semidirect |
| 4. #22561922 | C2 | semidirect |
| 5. C2×#16863198 | C2 | semidirect |
| 6. #22560994 | C2 | semidirect |
| 7. C67×#1379 | C2 | semidirect |
| 54. #14523979 | D4 | semidirect |
| 196. #1379 | D67 | semidirect |
| 197. C67 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570695 | 2 |
| C2×#16863210 | 2 |
| C2×#16863204 | 2 |
| #22561922 | 2 |
| C2×#16863198 | 2 |
| #22560994 | 2 |
| C67×#1379 | 2 |
| #13411 | 67 |