Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. C2×#16863812 | C2 | semidirect |
| 3. C2×#16863208 | C2 | semidirect |
| 4. C2×#16863198 | C2 | semidirect |
| 5. #22560270 | C2 | semidirect |
| 6. #22558319 | C2 | semidirect |
| 7. C67×#1381 | C2 | semidirect |
| 17. #16863667 | C4 | semidirect |
| 184. #1381 | D67 | semidirect |
| 185. C67 | #13073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863812 | 2 |
| C2×#16863667 | 2 |
| C2×#16863208 | 2 |
| C2×#16863198 | 2 |
| #22560270 | 2 |
| #22558319 | 2 |
| C67×#1381 | 2 |
| #13073 | 67 |