Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1434 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 181 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. #10596301 | C2 | semidirect |
| 2. C2×#64158 | C2 | semidirect |
| 3. C2×#64083 | C2 | semidirect |
| 4. C2×C32×#104 | C2 | semidirect |
| 5. #10592830 | C2 | semidirect |
| 6. C2×#63650 | C2 | semidirect |
| 7. #10589389 | C2 | semidirect |
| 33. C2×C3×#104 | D3 | semidirect |
| 43. C2×C32×Q8 | D4 | semidirect |
| 45. C2×C32×D4 | D4 | semidirect |
| 63. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 68. C32×C42 | D4 | semidirect |
| 73. C4⋊(C3⋊Dic3) | D4 | semidirect |
| 76. #3748 | D4 | semidirect |
| 143. C2×#104 | C3⋊D3 | semidirect |
| 153. C2×C3×Q8 | D12 | semidirect |
| 155. C2×C3×D4 | D12 | semidirect |
| 178. C3×C42 | #67 | semidirect |
| 283. C2×Q8 | C4⋊(C3⋊D3) | semidirect |
| 300. C2×D4 | C4⋊(C3⋊D3) | semidirect |
| 317. C42 | #638 | semidirect |
| 339. C32 | #2002 | semidirect |
| 408. C3 | #70385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596301 | 2 |
| C2×#64158 | 2 |
| C2×#64083 | 2 |
| C2×C32×#104 | 2 |
| #10592830 | 2 |
| C2×#63650 | 2 |
| #10589389 | 2 |
| #70385 | 3 |