Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
366 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562343 | C2 | semidirect |
| 3. #22559729 | C2 | semidirect |
| 4. #22558252 | C2 | semidirect |
| 5. #22558177 | C2 | semidirect |
| 6. #22558168 | C2 | semidirect |
| 7. C67×#2243 | C2 | semidirect |
| 18. C4⋊(C67⋊C16) | C22 | semidirect |
| 20. #16863147 | C22 | semidirect |
| 22. #500×C67 | C22 | semidirect |
| 26. #346×C67 | C22 | semidirect |
| 166. #2243 | D67 | semidirect |
| 172. C67 | #12376 | semidirect |
| 175. #500 | C2×D67 | semidirect |
| 189. #346 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571818 | 2 |
| #22562343 | 2 |
| #22559729 | 2 |
| #22558252 | 2 |
| #22558177 | 2 |
| #22558168 | 2 |
| C67×#2243 | 2 |
| #12376 | 67 |