Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
534 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22561197 | C2 | semidirect |
| 4. #22558891 | C2 | semidirect |
| 6. #22558498 | C2 | semidirect |
| 7. C67×#1567 | C2 | semidirect |
| 129. C8×C67 | #100 | semidirect |
| 157. #1567 | D67 | semidirect |
| 161. C67 | #9805 | semidirect |
| 285. C8 | #14523959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863769 | 2 |
| #22561197 | 2 |
| #22561048 | 2 |
| #22558891 | 2 |
| #22558878 | 2 |
| #22558498 | 2 |
| C67×#1567 | 2 |
| #9805 | 67 |