Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 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×#16863224 | C2 | semidirect |
| 3. C2×#16863198 | C2 | semidirect |
| 4. #22561075 | C2 | semidirect |
| 5. C2×#346×C67 | C2 | semidirect |
| 9. C2×D1072 | C4 | semidirect |
| 72. C16×C67 | C22⋊C4 | semidirect |
| 122. C2×#346 | D67 | semidirect |
| 124. C67 | #13239 | semidirect |
| 191. C16 | (C2×D67)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| C2×#16863224 | 2 |
| C2×#16863198 | 2 |
| #22561075 | 2 |
| C2×#346×C67 | 2 |
| #13239 | 67 |