Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 391 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. #22590634 | C2 | semidirect |
| 2. C2×#17985833 | C2 | semidirect |
| 5. #17985833 | C22 | semidirect |
| 6. C2×C71⋊C32 | C22 | semidirect |
| 59. C71 | #33974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590634 | 2 |
| C2×#17985833 | 2 |
| C2×#504×C71 | 2 |
| #33974 | 71 |