Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
214 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4⋊(C67⋊C32) | C2 | semidirect |
| 3. C22⋊(C67⋊C32) | C2 | semidirect |
| 4. C4×C67⋊C32 | C2 | semidirect |
| 17. C67⋊C32 | D4 | direct (N × H) |
| 43. D4×C67 | C32 | semidirect |
| 56. C22×C67 | C2×C32 | semidirect |
| 60. C4×C67 | C2×C32 | semidirect |
| 73. C67 | D4×C32 | semidirect |
| 111. D4 | C67⋊C32 | direct (N × H) |
| 124. C22 | C2×C67⋊C32 | semidirect |
| 128. C4 | C2×C67⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C67⋊C32 | 2 |
| C4⋊(C67⋊C32) | 2 |
| C22⋊(C67⋊C32) | 2 |
| C4×C67⋊C32 | 2 |
| D4×C16×C67 | 2 |
| D4×C32 | 67 |