Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 100 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×#4838 | C2 | semidirect |
| 3. #10590327 | C2 | semidirect |
| 4. #10589349 | C2 | semidirect |
| 5. C3×#4479 | C2 | semidirect |
| 6. #10589080 | C2 | semidirect |
| 7. #10589078 | C2 | semidirect |
| 27. #4838 | D3 | semidirect |
| 37. #4479 | D3 | semidirect |
| 100. C4⋊(C3⋊D3) | M16 | semidirect |
| 114. C3×C3⋊C8 | D8 | semidirect |
| 250. C3⋊C8 | #213 | semidirect |
| 313. C32 | #1581 | semidirect |
| 365. C3 | #68559 | semidirect |
| 366. C3 | #70862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4838 | 2 |
| C4×#3714 | 2 |
| #10590327 | 2 |
| #10589349 | 2 |
| C3×#4479 | 2 |
| #10589080 | 2 |
| #10589078 | 2 |
| #70862 | 3 |
| #68559 | 3 |