Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×C67⋊C32 | C2 | semidirect |
| 2. C2×C32×D67 | C2 | semidirect |
| 4. Dic67⋊C32 | C2 | semidirect |
| 5. (C2×D67)⋊C32 | C2 | semidirect |
| 6. C32×Dic67 | C2 | semidirect |
| 7. C67×C22⋊C32 | C2 | semidirect |
| 32. C67⋊C32 | D4 | semidirect |
| 66. C22⋊D67 | C32 | semidirect |
| 79. C22×C67 | C2×C32 | semidirect |
| 83. C2×D67 | C2×C32 | semidirect |
| 89. Dic67 | C2×C32 | semidirect |
| 101. C22⋊C32 | D67 | semidirect |
| 103. C67 | D4×C32 | semidirect |
| 178. C22 | C32×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C67⋊C32 | 2 |
| C2×C32×D67 | 2 |
| C16×C22⋊D67 | 2 |
| Dic67⋊C32 | 2 |
| (C2×D67)⋊C32 | 2 |
| C32×Dic67 | 2 |
| C67×C22⋊C32 | 2 |
| D4×C32 | 67 |