Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22561965 | C2 | semidirect |
| 3. C2×#16863208 | C2 | semidirect |
| 4. C4×#108×C67 | C2 | semidirect |
| 35. #108×C67 | D4 | semidirect |
| 95. C4×C67 | #361 | semidirect |
| 107. C4×#108 | D67 | semidirect |
| 108. C67 | #13257 | semidirect |
| 139. #108 | D268 | semidirect |
| 199. C4 | #16863208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863773 | 2 |
| #22561965 | 2 |
| C2×#16863208 | 2 |
| C4×#108×C67 | 2 |
| #13257 | 67 |