Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22562012 | C2 | semidirect |
| 3. #22558165 | C2 | semidirect |
| 4. C67×#2162 | C2 | semidirect |
| 13. C4⋊(C67⋊C16) | C22 | semidirect |
| 19. C4×C16×C67 | C22 | semidirect |
| 129. #2162 | D67 | semidirect |
| 131. C67 | #11631 | semidirect |
| 146. C4×C16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D268 | 2 |
| #22562012 | 2 |
| #22558165 | 2 |
| C67×#2162 | 2 |
| #11631 | 67 |