Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
508 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#16863204 | C2 | semidirect |
| 3. #22560247 | C2 | semidirect |
| 4. #22558305 | C2 | semidirect |
| 5. C23×C16×C67 | C2 | semidirect |
| 51. C2×C16×C67 | D4 | semidirect |
| 121. C22×C67 | #359 | semidirect |
| 138. C23×C16 | D67 | semidirect |
| 143. C67 | #13063 | semidirect |
| 182. C2×C16 | C22⋊D67 | semidirect |
| 261. C22 | #16863204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569790 | 2 |
| C2×#16863204 | 2 |
| #22560247 | 2 |
| #22558305 | 2 |
| C23×C16×C67 | 2 |
| #13063 | 67 |