Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1013 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 1013 conjugacy classes of subgroups — too many to draw. Only its 276 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 |
|---|---|---|
| 3. C3×#5125 | C2 | semidirect |
| 4. C2×#63578 | C2 | semidirect |
| 5. #10590914 | C2 | semidirect |
| 6. #10590913 | C2 | semidirect |
| 24. #5125 | D3 | semidirect |
| 221. C32 | #2916 | semidirect |
| 256. C3 | #79260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64116 | 2 |
| #10594780 | 2 |
| C3×#5125 | 2 |
| C2×#63578 | 2 |
| #10590914 | 2 |
| #10590913 | 2 |
| #79260 | 3 |