Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22561038 | C2 | semidirect |
| 3. #22561036 | C2 | semidirect |
| 4. #22560360 | C2 | semidirect |
| 5. #22558884 | C2 | semidirect |
| 6. #22558083 | C2 | semidirect |
| 7. C67×#1547 | C2 | semidirect |
| 99. C4×Dic67 | D8 | semidirect |
| 213. #1547 | D67 | semidirect |
| 215. C67 | #10518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571516 | 2 |
| #22561038 | 2 |
| #22561036 | 2 |
| #22560360 | 2 |
| #22558884 | 2 |
| #22558083 | 2 |
| C67×#1547 | 2 |
| #10518 | 67 |