Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
458 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 91 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×#16863218 | C2 | semidirect |
| 3. C2×#16863210 | C2 | semidirect |
| 4. C2×#16863208 | C2 | semidirect |
| 5. C2×#16863177 | C2 | semidirect |
| 6. #22560248 | C2 | semidirect |
| 7. C67×#1383 | C2 | semidirect |
| 46. #14523983 | D4 | semidirect |
| 178. #1383 | D67 | semidirect |
| 179. C67 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863650 | 2 |
| C2×#16863218 | 2 |
| C2×#16863210 | 2 |
| C2×#16863208 | 2 |
| C2×#16863177 | 2 |
| #22560248 | 2 |
| C67×#1383 | 2 |
| #13398 | 67 |