Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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. #22562297 | C2 | direct (N × H) |
| 4. C2×#16863222 | C2 | semidirect |
| 5. C2×#16863200 | C2 | semidirect |
| 6. C22×Q32×C67 | C2 | semidirect |
| 16. #16863222 | C22 | semidirect |
| 17. #16863200 | C22 | semidirect |
| 20. C2×Q32×C67 | C22 | semidirect |
| 82. C22×D67 | Q32 | semidirect |
| 111. C2×D67 | C2×Q32 | semidirect |
| 119. C2×C67 | #2216 | semidirect |
| 124. C22×Q32 | D67 | semidirect |
| 130. C67 | C2×#2216 | semidirect |
| 135. C2×Q32 | C2×D67 | semidirect |
| 243. C2 | #22562297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D67 | 2 |
| C2×#16863634 | 2 |
| #22562297 | 2 |
| C2×#16863222 | 2 |
| C2×#16863200 | 2 |
| C22×Q32×C67 | 2 |
| C2×#2216 | 67 |