Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#16863174 | C2 | semidirect |
| 3. #22558243 | C2 | semidirect |
| 4. #22558241 | C2 | semidirect |
| 5. C2×#347×C67 | C2 | semidirect |
| 141. C2×#347 | D67 | semidirect |
| 144. C67 | #11911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570555 | 2 |
| C2×#16863174 | 2 |
| #22558243 | 2 |
| #22558241 | 2 |
| C2×#347×C67 | 2 |
| #11911 | 67 |