Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 125 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. #10592571 | C2 | semidirect |
| 3. C32×#367 | C2 | semidirect |
| 4. #10589368 | C2 | semidirect |
| 5. #10589357 | C2 | semidirect |
| 14. #63626 | C4 | semidirect |
| 17. C3×#367 | D3 | semidirect |
| 28. #3745 | C2×C4 | semidirect |
| 29. C32×C16 | C2×C4 | semidirect |
| 52. #367 | C3⋊D3 | semidirect |
| 64. C3×C16 | C4×D3 | semidirect |
| 105. C16 | C4×C3⋊D3 | semidirect |
| 114. C32 | #2177 | semidirect |
| 136. C3 | #69339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63626 | 2 |
| #10592571 | 2 |
| C32×#367 | 2 |
| #10589368 | 2 |
| #10589357 | 2 |
| #69339 | 3 |