Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #22560957 | C2 | semidirect |
| 5. #22558305 | C2 | semidirect |
| 6. #22558303 | C2 | semidirect |
| 7. C2×#346×C67 | C2 | semidirect |
| 16. #16863201 | C4 | semidirect |
| 17. #16863198 | C4 | semidirect |
| 140. C2×#346 | D67 | semidirect |
| 145. C67 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863204 | 2 |
| #22561917 | 2 |
| #22561097 | 2 |
| #22560957 | 2 |
| #22558305 | 2 |
| #22558303 | 2 |
| C2×#346×C67 | 2 |
| #13152 | 67 |