Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4⋊(C71⋊C32) | C2 | semidirect |
| 2. C4×C71⋊C32 | C2 | semidirect |
| 39. D4×C71 | C32 | semidirect |
| 68. C71 | D4⋊C32 | semidirect |
| 104. D4 | C71⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C71⋊C32) | 2 |
| C4×C71⋊C32 | 2 |
| D4×C16×C71 | 2 |
| D4⋊C32 | 71 |