Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22561802 | C2 | semidirect |
| 3. #22558954 | C2 | semidirect |
| 4. #22558177 | C2 | semidirect |
| 5. #22558176 | C2 | semidirect |
| 6. #22558175 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 20. #16863172 | C22 | semidirect |
| 23. #16863147 | C22 | semidirect |
| 25. #346×C67 | C22 | semidirect |
| 26. #334×C67 | C22 | semidirect |
| 32. D8×D67 | C8 | semidirect |
| 173. #1333 | D67 | semidirect |
| 174. C67 | #11599 | semidirect |
| 189. #346 | C2×D67 | semidirect |
| 193. #334 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D67 | 2 |
| #22561802 | 2 |
| #22558954 | 2 |
| #22558177 | 2 |
| #22558176 | 2 |
| #22558175 | 2 |
| C67×#1333 | 2 |
| #11599 | 67 |