Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10590337 | C2 | semidirect |
| 3. #10590327 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 5. C3×#4459 | C2 | semidirect |
| 6. C3×#4455 | C2 | semidirect |
| 7. #10589097 | C2 | semidirect |
| 37. #4459 | D3 | semidirect |
| 39. #4455 | D3 | semidirect |
| 100. C4⋊(C3⋊D3) | M16 | semidirect |
| 313. C32 | #1586 | semidirect |
| 365. C3 | #68081 | semidirect |
| 366. C3 | #68158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3714 | 2 |
| #10590337 | 2 |
| #10590327 | 2 |
| #10589325 | 2 |
| C3×#4459 | 2 |
| C3×#4455 | 2 |
| #10589097 | 2 |
| #68158 | 3 |
| #68081 | 3 |