Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #22562433 | C2 | semidirect |
| 3. #22562356 | C2 | semidirect |
| 4. #22559609 | C2 | semidirect |
| 5. #22558254 | C2 | semidirect |
| 6. #22558165 | C2 | semidirect |
| 7. C67×#1331 | C2 | semidirect |
| 10. #16863801 | C22 | semidirect |
| 18. C4⋊(C67⋊C16) | C22 | semidirect |
| 23. C4×C16×C67 | C22 | semidirect |
| 24. #335×C67 | C22 | semidirect |
| 155. #1331 | D67 | semidirect |
| 157. C67 | #12372 | semidirect |
| 172. C4×C16 | C2×D67 | semidirect |
| 173. #335 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D268 | 2 |
| #22562433 | 2 |
| #22562356 | 2 |
| #22559609 | 2 |
| #22558254 | 2 |
| #22558165 | 2 |
| C67×#1331 | 2 |
| #12372 | 67 |