Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10590622 | C2 | semidirect |
| 3. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. C3×#4463 | C2 | semidirect |
| 5. #10589111 | C2 | semidirect |
| 25. #4463 | D3 | semidirect |
| 194. C32 | #2170 | semidirect |
| 221. C3 | #69300 | semidirect |
| 222. C3 | #70923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4700 | 2 |
| #10590622 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| C3×#4463 | 2 |
| #10589111 | 2 |
| #70923 | 3 |
| #69300 | 3 |