Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
431 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10590338 | C2 | semidirect |
| 3. #10590327 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. C3×#4454 | C2 | semidirect |
| 6. #10589082 | C2 | semidirect |
| 7. #10589082 | C2 | semidirect |
| 38. #4457 | D3 | semidirect |
| 39. #4454 | D3 | semidirect |
| 107. C4⋊(C3⋊D3) | M16 | semidirect |
| 332. C32 | #1586 | semidirect |
| 385. C3 | #68081 | semidirect |
| 386. C3 | #68521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| #10590338 | 2 |
| #10590327 | 2 |
| C3×#4457 | 2 |
| C3×#4454 | 2 |
| #10589082 | 2 |
| #68521 | 3 |
| #68081 | 3 |