Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22562484 | C2 | semidirect |
| 3. #22562436 | C2 | semidirect |
| 5. Q32×Dic67 | C2 | semidirect |
| 7. C67×#2247 | C2 | semidirect |
| 90. C4×D67 | Q32 | semidirect |
| 116. #2247 | D67 | semidirect |
| 121. C67 | #33734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570793 | 2 |
| #22562484 | 2 |
| #22562436 | 2 |
| #22562297 | 2 |
| Q32×Dic67 | 2 |
| C4×C16×D67 | 2 |
| C67×#2247 | 2 |
| #33734 | 67 |