Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
556 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10591637 | C2 | semidirect |
| 3. #10589408 | C2 | semidirect |
| 4. C3×#4542 | C2 | semidirect |
| 5. #10589182 | C2 | semidirect |
| 18. #63663 | C22 | semidirect |
| 19. C3×#836 | C22 | semidirect |
| 30. #4542 | D3 | semidirect |
| 81. #836 | C2×D3 | semidirect |
| 312. C32 | #2134 | semidirect |
| 368. C3 | #69166 | semidirect |
| 369. C3 | #71862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5674 | 2 |
| #10591637 | 2 |
| #10589408 | 2 |
| C3×#4542 | 2 |
| #10589182 | 2 |
| #71862 | 3 |
| #69166 | 3 |