Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1137 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1137 conjugacy classes of subgroups — too many to draw. Only its 228 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×#63919 | C2 | semidirect |
| 3. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 4. C2×C3×#821 | C2 | semidirect |
| 5. C2×#63562 | C2 | semidirect |
| 6. #10590885 | C2 | direct (N × H) |
| 18. #63919 | C22 | semidirect |
| 21. C8×C3⋊Dic3 | C22 | semidirect |
| 22. C3×#821 | C22 | semidirect |
| 23. #63562 | C22 | semidirect |
| 28. C2×#821 | D3 | semidirect |
| 78. #821 | C2×D3 | semidirect |
| 225. C2×C32 | #486 | semidirect |
| 282. C32 | C2×#486 | semidirect |
| 311. C2×C3 | #4760 | semidirect |
| 331. C3 | C2×#4760 | semidirect |
| 333. C2 | #10590885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63919 | 2 |
| C2×#63914 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×C3×#821 | 2 |
| C2×#63562 | 2 |
| #10590885 | 2 |
| C2×#4760 | 3 |