Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 385 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. #10590339 | C2 | semidirect |
| 3. #10589321 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. #10589080 | C2 | semidirect |
| 25. #4457 | D3 | semidirect |
| 75. C32×C8 | M16 | semidirect |
| 158. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 159. C3×C8 | #208 | semidirect |
| 206. C32 | #1594 | semidirect |
| 220. C8 | #3711 | semidirect |
| 242. C3 | #68525 | semidirect |
| 243. C3 | #70882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D24 | 2 |
| #10590339 | 2 |
| #10589321 | 2 |
| C3×#4457 | 2 |
| #10589080 | 2 |
| #70882 | 3 |
| #68525 | 3 |