Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 3. #22562348 | C2 | semidirect |
| 5. Q8⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558172 | C2 | semidirect |
| 7. C67×#1674 | C2 | semidirect |
| 132. #1674 | D67 | semidirect |
| 136. C67 | #12381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573222 | 2 |
| #22562434 | 2 |
| #22562348 | 2 |
| #22558254 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558172 | 2 |
| C67×#1674 | 2 |
| #12381 | 67 |