Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
676 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22565582 | C2 | semidirect |
| 4. C2×#16863126 | C2 | semidirect |
| 5. C67×#1296 | C2 | semidirect |
| 55. C2×Dic134 | SD16 | semidirect |
| 157. #1296 | D67 | semidirect |
| 158. C67 | #10230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863597 | 2 |
| #22565582 | 2 |
| #22561014 | 2 |
| C2×#16863126 | 2 |
| C67×#1296 | 2 |
| #10230 | 67 |