Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 165 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. C8×#634 | C2 | semidirect |
| 4. C32×#322 | C2 | semidirect |
| 6. #10589324 | C2 | semidirect |
| 7. #10589322 | C2 | semidirect |
| 27. C3×#322 | D3 | semidirect |
| 47. #3744 | C8 | semidirect |
| 77. #634 | C2×C8 | semidirect |
| 82. C32×C8 | C2×C8 | semidirect |
| 91. #322 | C3⋊D3 | semidirect |
| 154. C3×C8 | D3×C8 | semidirect |
| 191. C32 | SD16⋊C8 | semidirect |
| 211. C8 | C8×C3⋊D3 | semidirect |
| 228. C3 | #68076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3744 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| C8×#634 | 2 |
| C32×#322 | 2 |
| #10589325 | 2 |
| #10589324 | 2 |
| #10589322 | 2 |
| #68076 | 3 |