Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16863220 | C2 | semidirect |
| 5. #22558308 | C2 | semidirect |
| 6. #22558307 | C2 | semidirect |
| 7. C2×#365×C67 | C2 | semidirect |
| 18. (C2×D67)⋊C16 | C4 | semidirect |
| 40. C2×C67⋊C16 | C2×C4 | semidirect |
| 52. C2×C16×C67 | C2×C4 | semidirect |
| 134. C2×D67 | #365 | semidirect |
| 150. C2×#365 | D67 | semidirect |
| 155. C67 | #12929 | semidirect |
| 194. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#106×D67 | 2 |
| C2×#16863220 | 2 |
| #22561819 | 2 |
| #22560244 | 2 |
| #22558308 | 2 |
| #22558307 | 2 |
| C2×#365×C67 | 2 |
| #12929 | 67 |