Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
681 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 681 conjugacy classes of subgroups — too many to draw. Only its 84 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×C3×#827 | C2 | semidirect |
| 3. #10590857 | C2 | semidirect |
| 4. C2×#63549 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589108 | C2 | semidirect |
| 17. C2×C3×Dic12 | C22 | semidirect |
| 20. C3×#818 | C22 | semidirect |
| 21. C2×C3×C3⋊C16 | C22 | semidirect |
| 22. C2×C3×C3⋊C16 | C22 | semidirect |
| 31. C2×#827 | D3 | semidirect |
| 35. #4562 | D3 | semidirect |
| 82. C2×Dic12 | C2×D3 | semidirect |
| 97. #818 | C2×D3 | semidirect |
| 98. C2×C3⋊C16 | C2×D3 | semidirect |
| 99. C2×C3⋊C16 | C2×D3 | semidirect |
| 205. C2×C3⋊D3 | SD32 | semidirect |
| 364. C32 | #2187 | semidirect |
| 422. C3 | #69193 | semidirect |
| 423. C3 | #71485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C3⋊D3 | 2 |
| C2×C3×#827 | 2 |
| #10590857 | 2 |
| C2×#63549 | 2 |
| C3×#4562 | 2 |
| #10589116 | 2 |
| #10589108 | 2 |
| #71485 | 3 |
| #69193 | 3 |