Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
202 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 107 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. Dic67⋊C32 | C2 | semidirect |
| 4. C4×C67⋊C32 | C2 | semidirect |
| 5. C4×C32×C67 | C2 | semidirect |
| 58. C4×D67 | C32 | semidirect |
| 84. C4×C32 | D67 | semidirect |
| 85. C67 | #13639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D67 | 2 |
| Dic67⋊C32 | 2 |
| (C2×D67)⋊C32 | 2 |
| C4×C67⋊C32 | 2 |
| C4×C32×C67 | 2 |
| #13639 | 67 |