Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22561053 | C2 | semidirect |
| 4. #22558968 | C2 | semidirect |
| 5. #22558880 | C2 | semidirect |
| 7. C8×M16×C67 | C2 | semidirect |
| 160. C8×M16 | D67 | semidirect |
| 161. C67 | #9796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863743 | 2 |
| #22561053 | 2 |
| #22561049 | 2 |
| #22558968 | 2 |
| #22558880 | 2 |
| #22558876 | 2 |
| C8×M16×C67 | 2 |
| #9796 | 67 |