Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #10590812 | C2 | semidirect |
| 4. #10589379 | C2 | semidirect |
| 5. C3×#4512 | C2 | semidirect |
| 6. #10589130 | C2 | semidirect |
| 19. C3×Dic24 | C4 | semidirect |
| 20. C3×#800 | C4 | semidirect |
| 37. #4512 | D3 | semidirect |
| 84. Dic24 | Dic3 | semidirect |
| 85. #800 | Dic3 | semidirect |
| 242. C32 | #2180 | semidirect |
| 274. C3 | #69090 | semidirect |
| 275. C3 | #71521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4909 | 2 |
| #10590916 | 2 |
| #10590812 | 2 |
| #10589379 | 2 |
| C3×#4512 | 2 |
| #10589130 | 2 |
| #10589124 | 2 |
| #71521 | 3 |
| #69090 | 3 |