Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
442 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22562465 | C2 | semidirect |
| 3. #22562255 | C2 | semidirect |
| 4. #22559574 | C2 | semidirect |
| 5. #22558256 | C2 | semidirect |
| 6. #22558171 | C2 | semidirect |
| 7. C67×D4⋊C16 | C2 | semidirect |
| 12. #16863776 | C22 | semidirect |
| 20. #16863149 | C22 | semidirect |
| 23. C4⋊C16×C67 | C22 | semidirect |
| 24. C4×C16×C67 | C22 | semidirect |
| 103. D4×C67 | SD32 | semidirect |
| 162. D4⋊C16 | D67 | semidirect |
| 163. C67 | #12320 | semidirect |
| 176. C4⋊C16 | C2×D67 | semidirect |
| 178. C4×C16 | C2×D67 | semidirect |
| 270. D4 | #14523988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D536 | 2 |
| #22562465 | 2 |
| #22562255 | 2 |
| #22559574 | 2 |
| #22558256 | 2 |
| #22558171 | 2 |
| C67×D4⋊C16 | 2 |
| #12320 | 67 |