Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
558 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C22×#14523983 | C2 | semidirect |
| 3. C2×#16863196 | C2 | semidirect |
| 4. #22558300 | C2 | semidirect |
| 5. C67×#1808 | C2 | semidirect |
| 12. #16863632 | C4 | semidirect |
| 33. C2×C67⋊C16 | D4 | semidirect |
| 149. #1808 | D67 | semidirect |
| 151. C67 | #13061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523983 | 2 |
| C2×#16863632 | 2 |
| C2×#16863196 | 2 |
| #22558300 | 2 |
| C67×#1808 | 2 |
| #13061 | 67 |