Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
359 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 359 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 |
|---|---|---|
| 3. #10590296 | C2 | semidirect |
| 4. #10589350 | C2 | semidirect |
| 5. C3×#4479 | C2 | semidirect |
| 7. #10589078 | C2 | semidirect |
| 37. #4479 | D3 | semidirect |
| 111. C3×C3⋊C8 | M16 | semidirect |
| 237. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 292. C32 | #1592 | semidirect |
| 337. C3 | #68565 | semidirect |
| 338. C3 | #70860 | 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×#4479 | 2 |
| #10589080 | 2 |
| #10589078 | 2 |
| #70860 | 3 |
| #68565 | 3 |