Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
128 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 46 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. #11757430 | C2 | direct (N × H) |
| 18. C2×C22⋊C27 | C9 | semidirect |
| 33. C22⋊C27 | C2×C9 | semidirect |
| 96. C23 | #6875 | semidirect |
| 105. C22 | C2×#6875 | semidirect |
| 110. C2 | #11757430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757430 | 2 |
| C23×C27⋊C3 | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×#66353 | 3 |
| C2×#6875 | 4 |