Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1225 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 200 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×#63809 | C2 | semidirect |
| 2. #10593907 | C2 | semidirect |
| 3. C4×C8×C3⋊D3 | C2 | semidirect |
| 4. C3×#4693 | C2 | semidirect |
| 5. #10590867 | C2 | semidirect |
| 6. #10590387 | C2 | semidirect |
| 7. #10590352 | C2 | semidirect |
| 31. #4693 | D3 | semidirect |
| 47. C8×C3⋊D3 | D4 | semidirect |
| 145. C32×C4 | #135 | semidirect |
| 233. C3×C4 | #916 | semidirect |
| 240. C32 | #3147 | semidirect |
| 273. C4 | #63809 | semidirect |
| 276. C3 | #81760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63809 | 2 |
| #10593907 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C3×#4693 | 2 |
| #10590867 | 2 |
| #10590387 | 2 |
| #10590352 | 2 |
| #81760 | 3 |