Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
858 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×C32×#99 | C2 | semidirect |
| 3. C2×#63661 | C2 | semidirect |
| 4. #10589340 | C2 | semidirect |
| 5. #10589339 | C2 | semidirect |
| 8. C2×#3828 | C4 | semidirect |
| 13. #64149 | C4 | semidirect |
| 17. #64145 | C4 | semidirect |
| 19. #64135 | C4 | semidirect |
| 25. C2×C3×#99 | D3 | semidirect |
| 47. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 49. C2×#634 | C2×C4 | semidirect |
| 60. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 61. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 118. C2×#99 | C3⋊D3 | semidirect |
| 301. C32 | #2127 | semidirect |
| 373. C3 | #70019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596276 | 2 |
| C2×C32×#99 | 2 |
| C2×#63661 | 2 |
| #10589340 | 2 |
| #10589339 | 2 |
| #70019 | 3 |