Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
726 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 145 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. C32×#493 | C2 | semidirect |
| 2. #10592775 | C2 | semidirect |
| 3. #10592772 | C2 | semidirect |
| 4. #10592772 | C2 | semidirect |
| 5. #10592769 | C2 | semidirect |
| 6. #10592393 | C2 | semidirect |
| 7. #10589320 | C2 | semidirect |
| 22. C3×#493 | D3 | semidirect |
| 82. C3⋊(C3⋊C8) | D8 | semidirect |
| 85. #493 | C3⋊D3 | semidirect |
| 197. C32 | #1721 | semidirect |
| 238. C3 | #71279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| #10592775 | 2 |
| #10592772 | 2 |
| #10592769 | 2 |
| #10592393 | 2 |
| #10589320 | 2 |
| #71279 | 3 |