Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×C4×D24 | C2 | semidirect |
| 3. #10589327 | C2 | semidirect |
| 4. #10589142 | C2 | semidirect |
| 5. #10589114 | C2 | semidirect |
| 14. #63545 | C4 | semidirect |
| 17. C4×D24 | D3 | semidirect |
| 31. C3×D24 | C2×C4 | semidirect |
| 33. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 82. D24 | C4×D3 | semidirect |
| 155. C32 | #2177 | semidirect |
| 182. C3 | #70885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D24 | 2 |
| C2×#63545 | 2 |
| #10589327 | 2 |
| #10589142 | 2 |
| #10589114 | 2 |
| #70885 | 3 |