Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. C32×#367 | C2 | semidirect |
| 5. #10589370 | C2 | semidirect |
| 6. #10589356 | C2 | semidirect |
| 7. #10589355 | C2 | semidirect |
| 20. #63625 | C4 | semidirect |
| 24. C3×#367 | D3 | semidirect |
| 41. C32×C16 | C2×C4 | semidirect |
| 42. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 73. #367 | C3⋊D3 | semidirect |
| 89. C3×C16 | C4×D3 | semidirect |
| 145. C16 | C4×C3⋊D3 | semidirect |
| 157. C32 | #2159 | semidirect |
| 186. C3 | #69346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63625 | 2 |
| #10592579 | 2 |
| C3⋊D3×#107 | 2 |
| C32×#367 | 2 |
| #10589370 | 2 |
| #10589356 | 2 |
| #10589355 | 2 |
| #69346 | 3 |