Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
388 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22558379 | C2 | semidirect |
| 5. #16863953 | C4 | semidirect |
| 6. #16863760 | C4 | semidirect |
| 13. C4×#11761612 | C4 | semidirect |
| 22. #14524035 | C2×C4 | semidirect |
| 33. #14523954 | C2×C4 | semidirect |
| 155. C67 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570583 | 2 |
| C2×#16863189 | 2 |
| #22558379 | 2 |
| C2×#353×C67 | 2 |
| #13595 | 67 |