Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
450 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22561894 | C2 | semidirect |
| 3. #22558375 | C2 | semidirect |
| 4. C67×#2132 | C2 | semidirect |
| 14. #16863195 | C22 | semidirect |
| 18. #356×C67 | C22 | semidirect |
| 158. #2132 | D67 | semidirect |
| 160. C67 | #13591 | semidirect |
| 173. #356 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570662 | 2 |
| #22561894 | 2 |
| #22558375 | 2 |
| C67×#2132 | 2 |
| #13591 | 67 |