Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1225 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 236 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. C3×#5477 | C2 | semidirect |
| 2. C2×#63822 | C2 | semidirect |
| 3. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10590387 | C2 | semidirect |
| 5. #10590375 | C2 | semidirect |
| 6. #10590353 | C2 | semidirect |
| 7. #10590352 | C2 | semidirect |
| 26. #5477 | D3 | semidirect |
| 45. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 147. C32×C4 | #135 | semidirect |
| 237. C3×C4 | #950 | semidirect |
| 240. C32 | #3147 | semidirect |
| 272. C4 | #63822 | semidirect |
| 276. C3 | #83285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5477 | 2 |
| C2×#63822 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10590387 | 2 |
| #10590375 | 2 |
| #10590353 | 2 |
| #10590352 | 2 |
| #83285 | 3 |