Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
461 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 176 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. #10589321 | C2 | semidirect |
| 4. C3×C8×C3⋊C8 | C2 | semidirect |
| 5. #10589078 | C2 | semidirect |
| 27. C8×C3⋊C8 | D3 | semidirect |
| 67. C32×C8 | M16 | semidirect |
| 70. C3×C3⋊C8 | M16 | semidirect |
| 136. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 137. C3×C8 | #208 | semidirect |
| 142. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 174. C32 | #1455 | semidirect |
| 185. C8 | #3711 | semidirect |
| 202. C3 | #68050 | semidirect |
| 203. C3 | #69849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×ΓL(1,𝔽25) | 2 |
| C4×#3711 | 2 |
| #10589321 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #10589078 | 2 |
| #69849 | 3 |
| #68050 | 3 |