Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 1. C2×#16863225 | C2 | semidirect |
| 2. C2×#16863209 | C2 | semidirect |
| 3. C2×#16863197 | C2 | semidirect |
| 4. #22561823 | C2 | semidirect |
| 5. #22560273 | C2 | semidirect |
| 6. #22558319 | C2 | semidirect |
| 178. C67 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863225 | 2 |
| C2×#16863209 | 2 |
| C2×#16863197 | 2 |
| #22561823 | 2 |
| #22560273 | 2 |
| #22558319 | 2 |
| C2×#472×C67 | 2 |
| #13393 | 67 |