Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
411 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 411 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. C4×#3745 | C2 | semidirect |
| 2. C3×C4×D24 | C2 | semidirect |
| 4. C3×#4461 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 21. #63546 | C4 | semidirect |
| 28. C4×D24 | D3 | semidirect |
| 36. #4461 | D3 | semidirect |
| 47. #3745 | C2×C4 | semidirect |
| 51. C3×D24 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 145. D24 | C4×D3 | semidirect |
| 149. C3⋊C16 | C4×D3 | semidirect |
| 275. C32 | #2177 | semidirect |
| 320. C3 | #69078 | semidirect |
| 321. C3 | #70885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C3×C4×D24 | 2 |
| C2×#63546 | 2 |
| C3×#4461 | 2 |
| #10589141 | 2 |
| #10589116 | 2 |
| #10589115 | 2 |
| #70885 | 3 |
| #69078 | 3 |