Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
138 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 59 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. C4⋊(C71⋊C32) | C2 | semidirect |
| 3. C4×C32×C71 | C2 | semidirect |
| 43. D284 | C32 | semidirect |
| 67. C4×C32 | D71 | semidirect |
| 68. C71 | D4⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D284 | 2 |
| C4⋊(C71⋊C32) | 2 |
| C4×C32×C71 | 2 |
| D4⋊C32 | 71 |