Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22559802 | C2 | semidirect |
| 3. D8×C67⋊C8 | C2 | semidirect |
| 4. #22558272 | C2 | semidirect |
| 5. #22558264 | C2 | semidirect |
| 6. #22558256 | C2 | semidirect |
| 7. C67×#2224 | C2 | semidirect |
| 63. D8×C67 | SD16 | semidirect |
| 96. C67⋊C8 | D16 | semidirect |
| 117. #2224 | D67 | semidirect |
| 124. C67 | #12416 | semidirect |
| 174. D8 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562244 | 2 |
| #22559802 | 2 |
| D8×C67⋊C8 | 2 |
| #22558272 | 2 |
| #22558264 | 2 |
| #22558256 | 2 |
| C67×#2224 | 2 |
| #12416 | 67 |