Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
557 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 557 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C2×#63627 | C2 | semidirect |
| 3. #10590852 | C2 | semidirect |
| 4. C2×#63548 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 7. #10589116 | C2 | semidirect |
| 11. C2×#3746 | C22 | semidirect |
| 19. C2×C32×C16 | C22 | semidirect |
| 21. C3×#818 | C22 | semidirect |
| 22. C2×C3×C3⋊C16 | C22 | semidirect |
| 37. #4509 | D3 | semidirect |
| 38. (C2×D3)⋊C16 | D3 | semidirect |
| 87. C2×C3×C16 | C2×D3 | semidirect |
| 88. C2×C3×C16 | C2×D3 | semidirect |
| 91. #818 | C2×D3 | semidirect |
| 93. C2×C3⋊C16 | C2×D3 | semidirect |
| 193. C2×C3×D3 | SD32 | semidirect |
| 212. C2×C16 | D32 | semidirect |
| 323. C2×D3 | #800 | semidirect |
| 337. C32 | #2187 | semidirect |
| 393. C3 | #69110 | semidirect |
| 394. C3 | #69193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D24 | 2 |
| C2×#63627 | 2 |
| #10590852 | 2 |
| C2×#63548 | 2 |
| C3×#4509 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| #10589116 | 2 |
| #69193 | 3 |
| #69110 | 3 |