Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22561150 | C2 | semidirect |
| 4. #22558612 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 7. C67×#3104 | C2 | semidirect |
| 194. #3104 | D67 | semidirect |
| 200. C67 | #10035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570557 | 2 |
| #22570240 | 2 |
| #22561150 | 2 |
| #22558612 | 2 |
| #22558609 | 2 |
| #22558039 | 2 |
| C67×#3104 | 2 |
| #10035 | 67 |