Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1716 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 277 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×#64128 | C2 | semidirect |
| 2. #10596196 | C2 | semidirect |
| 3. C32×#494 | C2 | semidirect |
| 4. #10592890 | C2 | semidirect |
| 5. #10592784 | C2 | semidirect |
| 6. #10592394 | C2 | semidirect |
| 7. C4×C8×C3⋊D3 | C2 | semidirect |
| 26. C3×#494 | D3 | semidirect |
| 49. C8×C3⋊D3 | D4 | semidirect |
| 85. #494 | C3⋊D3 | semidirect |
| 114. C32×C4 | #135 | semidirect |
| 178. C3×C4 | #919 | semidirect |
| 182. C32 | #3147 | semidirect |
| 211. C4 | #64128 | semidirect |
| 213. C3 | #81799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64128 | 2 |
| #10596196 | 2 |
| C32×#494 | 2 |
| #10592890 | 2 |
| #10592784 | 2 |
| #10592394 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #81799 | 3 |