Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
480 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#16863212 | C2 | semidirect |
| 5. #22558304 | C2 | semidirect |
| 6. #22558298 | C2 | semidirect |
| 7. C67×#2950 | C2 | semidirect |
| 11. C2×#14523986 | C4 | semidirect |
| 161. #2950 | D67 | semidirect |
| 167. C67 | #13018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523986 | 2 |
| C2×#16863212 | 2 |
| #22561924 | 2 |
| #22561119 | 2 |
| #22558304 | 2 |
| #22558298 | 2 |
| C67×#2950 | 2 |
| #13018 | 67 |