Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
476 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22562128 | C2 | semidirect |
| 3. #22561219 | C2 | semidirect |
| 4. #22558219 | C2 | semidirect |
| 5. C67×#1314 | C2 | semidirect |
| 6. C22×Dic268 | C22 | semidirect |
| 16. #16863159 | C22 | semidirect |
| 18. C22⋊C16×C67 | C22 | semidirect |
| 94. C23×C67 | SD32 | semidirect |
| 162. #1314 | D67 | semidirect |
| 163. C67 | #12105 | semidirect |
| 175. C22⋊C16 | C2×D67 | semidirect |
| 256. C23 | #14523988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570960 | 2 |
| #22562128 | 2 |
| #22561219 | 2 |
| #22558219 | 2 |
| C67×#1314 | 2 |
| #12105 | 67 |