Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16863231 | C2 | semidirect |
| 2. #22562295 | C2 | semidirect |
| 3. #22558387 | C2 | semidirect |
| 4. C22⋊(C67⋊C32) | C2 | semidirect |
| 5. C22×D16×C67 | C2 | semidirect |
| 6. C2×D1072 | C22 | semidirect |
| 9. C2×C67⋊C32 | C22 | semidirect |
| 10. #16863222 | C22 | semidirect |
| 31. D16×C67 | D4 | semidirect |
| 82. C22×C67 | D32 | semidirect |
| 98. C22×D16 | D67 | semidirect |
| 103. C67 | #13661 | semidirect |
| 126. D16 | C22⋊D67 | semidirect |
| 183. C22 | #16863231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863231 | 2 |
| #22562295 | 2 |
| #22558387 | 2 |
| C22⋊(C67⋊C32) | 2 |
| C22×D16×C67 | 2 |
| #13661 | 67 |