Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
254 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 78 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. C22×#6872 | C2 | semidirect |
| 2. C2×#92181 | C2 | direct (N × H) |
| 5. C2×#6872 | C22 | semidirect |
| 6. #92181 | C22 | direct (N × H) |
| 10. C22×C3×C27 | D3 | semidirect |
| 12. #6872 | C23 | semidirect |
| 20. C2×C3×C27 | C2×D3 | semidirect |
| 35. C3×C27 | C22×D3 | semidirect |
| 95. C22 | #92181 | direct (N × H) |
| 100. C2 | C2×#92181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6872 | 2 |
| C2×#92181 | 2 |
| C22×#4208 | 3 |
| C22×D3×C27 | 3 |