Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1225 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 232 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. #10595223 | C2 | semidirect |
| 3. C3×#5152 | C2 | semidirect |
| 4. #10591426 | C2 | semidirect |
| 5. #10591400 | C2 | semidirect |
| 6. #10590768 | C2 | semidirect |
| 7. #10590712 | C2 | semidirect |
| 8. #10590703 | C2 | semidirect |
| 13. D8×C3⋊D3 | C4 | semidirect |
| 16. C3×D4×Dic3 | C22 | semidirect |
| 20. #63894 | C22 | semidirect |
| 24. C3×#832 | C22 | semidirect |
| 25. C3×#817 | C22 | semidirect |
| 26. C3×#815 | C22 | semidirect |
| 27. #63576 | C22 | semidirect |
| 28. #63564 | C22 | semidirect |
| 29. Dic3×C3⋊C8 | C22 | semidirect |
| 34. #5152 | D3 | semidirect |
| 46. D4×C3⋊D3 | C2×C4 | semidirect |
| 51. C32×D8 | C2×C4 | semidirect |
| 53. #3753 | C2×C4 | semidirect |
| 55. #3745 | C2×C4 | semidirect |
| 56. C8×C3⋊D3 | C2×C4 | semidirect |
| 73. D4×Dic3 | C2×D3 | semidirect |
| 94. #832 | C2×D3 | semidirect |
| 96. #817 | C2×D3 | semidirect |
| 97. #815 | C2×D3 | semidirect |
| 150. C3×D8 | C4×D3 | semidirect |
| 268. D8 | #624 | semidirect |
| 310. C32 | #2948 | semidirect |
| 356. C3 | #79867 | 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 |
| #10595223 | 2 |
| C3×#5152 | 2 |
| #10591426 | 2 |
| #10591400 | 2 |
| #10590768 | 2 |
| #10590712 | 2 |
| #10590703 | 2 |
| #79867 | 3 |