Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 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. #22561969 | C2 | semidirect |
| 3. C2×#16863213 | C2 | semidirect |
| 4. #22561122 | C2 | semidirect |
| 6. #22558302 | C2 | semidirect |
| 161. C67 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523987 | 2 |
| #22561969 | 2 |
| C2×#16863213 | 2 |
| #22561122 | 2 |
| #22561120 | 2 |
| #22558302 | 2 |
| C2×#361×C67 | 2 |
| #13440 | 67 |