Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #22562291 | C2 | semidirect |
| 3. #22562290 | C2 | semidirect |
| 4. #22559815 | C2 | semidirect |
| 5. #22558245 | C2 | semidirect |
| 6. #22558183 | C2 | semidirect |
| 7. C67×#1335 | C2 | semidirect |
| 12. #16863776 | C22 | semidirect |
| 19. #16863217 | C22 | semidirect |
| 23. #364×C67 | C22 | semidirect |
| 24. C82×C67 | C22 | semidirect |
| 151. #1335 | D67 | semidirect |
| 152. C67 | #12312 | semidirect |
| 166. #364 | C2×D67 | semidirect |
| 169. C82 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572009 | 2 |
| #22562291 | 2 |
| #22562290 | 2 |
| #22559815 | 2 |
| #22558245 | 2 |
| #22558183 | 2 |
| C67×#1335 | 2 |
| #12312 | 67 |