Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
367 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #10590296 | C2 | semidirect |
| 4. #10589350 | C2 | semidirect |
| 5. C3×#4480 | C2 | semidirect |
| 7. C3⋊C82 | C2 | semidirect |
| 37. #4480 | D3 | semidirect |
| 110. C3×C3⋊C8 | M16 | semidirect |
| 111. C3×C3⋊C8 | SD16 | semidirect |
| 236. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 237. C3⋊C8 | #214 | semidirect |
| 292. C32 | #1590 | semidirect |
| 337. C3 | #68523 | semidirect |
| 338. C3 | #70866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4838 | 2 |
| C4×#3716 | 2 |
| #10590296 | 2 |
| #10589350 | 2 |
| C3×#4480 | 2 |
| #10589080 | 2 |
| C3⋊C82 | 2 |
| #70866 | 3 |
| #68523 | 3 |