Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
502 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 502 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 |
|---|---|---|
| 2. #22560982 | C2 | semidirect |
| 3. #22558878 | C2 | semidirect |
| 4. C2×#16863139 | C2 | semidirect |
| 5. #22558608 | C2 | semidirect |
| 6. #22558059 | C2 | semidirect |
| 7. C67×#1547 | C2 | semidirect |
| 202. #1547 | D67 | semidirect |
| 207. C67 | #10549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570662 | 2 |
| #22560982 | 2 |
| #22558878 | 2 |
| C2×#16863139 | 2 |
| #22558608 | 2 |
| #22558059 | 2 |
| C67×#1547 | 2 |
| #10549 | 67 |