Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
204 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#16863229 | C2 | semidirect |
| 3. Dic67⋊C32 | C2 | semidirect |
| 4. C22⋊(C67⋊C32) | C2 | semidirect |
| 5. (C2×D67)⋊C32 | C2 | semidirect |
| 6. #22558342 | C2 | semidirect |
| 7. C22×C32×C67 | C2 | semidirect |
| 39. C32×C67 | D4 | semidirect |
| 79. C22×C67 | M64 | semidirect |
| 97. C22×C32 | D67 | semidirect |
| 103. C67 | #13645 | semidirect |
| 135. C32 | C22⋊D67 | semidirect |
| 178. C22 | #16863229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863229 | 2 |
| C16×C22⋊D67 | 2 |
| Dic67⋊C32 | 2 |
| C22⋊(C67⋊C32) | 2 |
| (C2×D67)⋊C32 | 2 |
| #22558342 | 2 |
| C22×C32×C67 | 2 |
| #13645 | 67 |