Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22561982 | C2 | semidirect |
| 3. #22561946 | C2 | semidirect |
| 4. #22561917 | C2 | semidirect |
| 5. #22560255 | C2 | semidirect |
| 6. #22558305 | C2 | semidirect |
| 7. C2×#350×C67 | C2 | semidirect |
| 180. C2×#350 | D67 | semidirect |
| 183. C67 | #13401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569929 | 2 |
| #22561982 | 2 |
| #22561946 | 2 |
| #22561917 | 2 |
| #22560255 | 2 |
| #22558305 | 2 |
| C2×#350×C67 | 2 |
| #13401 | 67 |