Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562448 | C2 | semidirect |
| 3. #22562353 | C2 | semidirect |
| 4. #22558251 | C2 | semidirect |
| 5. #22558175 | C2 | semidirect |
| 6. #22558167 | C2 | semidirect |
| 7. C67×#1693 | C2 | semidirect |
| 17. C4⋊(C67⋊C16) | C22 | semidirect |
| 21. #16863172 | C22 | semidirect |
| 22. #500×C67 | C22 | semidirect |
| 25. #334×C67 | C22 | semidirect |
| 82. D536 | SD16 | semidirect |
| 170. #1693 | D67 | semidirect |
| 174. C67 | #12378 | semidirect |
| 177. #500 | C2×D67 | semidirect |
| 192. #334 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571821 | 2 |
| #22562448 | 2 |
| #22562353 | 2 |
| #22558251 | 2 |
| #22558175 | 2 |
| #22558167 | 2 |
| C67×#1693 | 2 |
| #12378 | 67 |