Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
458 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22571884 | C2 | semidirect |
| 2. #22562241 | C2 | semidirect |
| 3. #22559561 | C2 | semidirect |
| 4. #22558255 | C2 | semidirect |
| 5. #22558171 | C2 | semidirect |
| 6. #22558165 | C2 | semidirect |
| 7. C67×#2246 | C2 | semidirect |
| 17. C4⋊(C67⋊C16) | C22 | semidirect |
| 19. #16863149 | C22 | semidirect |
| 23. #493×C67 | C22 | semidirect |
| 24. C4×C16×C67 | C22 | semidirect |
| 68. D536 | D8 | semidirect |
| 124. D268 | D16 | semidirect |
| 164. #2246 | D67 | semidirect |
| 170. C67 | #12316 | semidirect |
| 176. #493 | C2×D67 | semidirect |
| 185. C4×C16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571884 | 2 |
| #22562241 | 2 |
| #22559561 | 2 |
| #22558255 | 2 |
| #22558171 | 2 |
| #22558165 | 2 |
| C67×#2246 | 2 |
| #12316 | 67 |