Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×D16×D67 | C2 | semidirect |
| 2. C2×D2144 | C2 | semidirect |
| 3. C2×#16863231 | C2 | semidirect |
| 4. #22562296 | C2 | semidirect |
| 5. #22558386 | C2 | semidirect |
| 6. (C2×D67)⋊C32 | C2 | semidirect |
| 7. C67×#1415 | C2 | semidirect |
| 10. C2×D1072 | C22 | semidirect |
| 18. C2×C67⋊C32 | C22 | semidirect |
| 21. C2×C32×C67 | C22 | semidirect |
| 22. #366×C67 | C22 | semidirect |
| 34. D1072 | D4 | semidirect |
| 43. D16×C67 | D4 | semidirect |
| 108. C2×D67 | D32 | semidirect |
| 126. #1415 | D67 | semidirect |
| 128. C67 | #13661 | semidirect |
| 141. C2×C32 | C2×D67 | semidirect |
| 142. #366 | C2×D67 | semidirect |
| 159. D16 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D67 | 2 |
| C2×D2144 | 2 |
| C2×#16863231 | 2 |
| #22562296 | 2 |
| #22558386 | 2 |
| (C2×D67)⋊C32 | 2 |
| C67×#1415 | 2 |
| #13661 | 67 |