Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
156 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 39 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. C2×#92182 | C2 | semidirect |
| 2. C4×#6872 | C2 | semidirect |
| 4. C4⋊(C3⋊D27) | C3 | semidirect |
| 9. C2×C3⋊D27 | C2×C3 | semidirect |
| 11. C3×C4×C27 | C2×C3 | semidirect |
| 12. #6872 | D4 | semidirect |
| 37. C3×C27 | C3×D4 | semidirect |
| 101. C4 | #92182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92182 | 2 |
| C4×#6872 | 2 |
| C4⋊#4207 | 3 |
| C4⋊(C3⋊D27) | 3 |