Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11757634 | C2 | direct (N × H) |
| 3. C2×C3⋊(C3⋊Dic9) | C3 | semidirect |
| 8. C2×#6908 | C4 | semidirect |
| 13. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 24. #6908 | C2×C4 | semidirect |
| 36. C2×#737 | Dic3 | semidirect |
| 38. C2×C32×C9 | C3×C4 | semidirect |
| 42. C2×#732 | Dic3 | semidirect |
| 46. C2×#731 | Dic3 | semidirect |
| 77. #737 | C2×Dic3 | semidirect |
| 78. C32×C9 | C2×C3×C4 | semidirect |
| 80. #732 | C2×Dic3 | semidirect |
| 82. #731 | C2×Dic3 | semidirect |
| 225. C2 | #11757634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6908 | 2 |
| #11757634 | 2 |
| C2×C3⋊(C3⋊Dic9) | 3 |
| C2×#66409 | 3 |
| C2×#66326 | 3 |
| C2×#66324 | 3 |
| C2×#66322 | 3 |