Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22561813 | C2 | semidirect |
| 5. #22560990 | C2 | semidirect |
| 6. #22558314 | C2 | semidirect |
| 7. C67×#1389 | C2 | semidirect |
| 15. #16863211 | C4 | semidirect |
| 16. #16863208 | C4 | semidirect |
| 145. #1389 | D67 | semidirect |
| 147. C67 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561956 | 2 |
| C2×#16863207 | 2 |
| #22561813 | 2 |
| #22561105 | 2 |
| #22560990 | 2 |
| #22558314 | 2 |
| C67×#1389 | 2 |
| #13156 | 67 |