Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
806 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 806 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 |
|---|---|---|
| 1. C22×C16×D67 | C2 | semidirect |
| 2. C2×#16863629 | C2 | semidirect |
| 3. #22562292 | C2 | direct (N × H) |
| 4. C2×#16863222 | C2 | semidirect |
| 5. C2×#16863197 | C2 | semidirect |
| 6. C22×D16×C67 | C2 | semidirect |
| 11. C2×C16×D67 | C22 | semidirect |
| 13. #16863629 | C22 | semidirect |
| 16. #16863222 | C22 | semidirect |
| 17. #16863197 | C22 | semidirect |
| 20. C2×D16×C67 | C22 | semidirect |
| 46. C2×C16×C67 | D4 | semidirect |
| 79. C16×C67 | C2×D4 | semidirect |
| 87. C22×D67 | D16 | semidirect |
| 119. C2×D67 | C2×D16 | semidirect |
| 127. C2×C67 | #2215 | semidirect |
| 132. C22×D16 | D67 | semidirect |
| 138. C67 | C2×#2215 | semidirect |
| 143. C2×D16 | C2×D67 | semidirect |
| 175. C2×C16 | C22⋊D67 | semidirect |
| 211. C16 | C2×C22⋊D67 | semidirect |
| 259. C2 | #22562292 | 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×#16863629 | 2 |
| #22562292 | 2 |
| C2×#16863222 | 2 |
| C2×#16863197 | 2 |
| C22×D16×C67 | 2 |
| C2×#2215 | 67 |