Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 168 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. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C3×#4455 | C2 | semidirect |
| 5. #10589079 | C2 | semidirect |
| 22. #4455 | D3 | semidirect |
| 67. C32×C8 | M16 | semidirect |
| 68. C3⋊(C3⋊C8) | M16 | semidirect |
| 136. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 137. C3×C8 | #208 | semidirect |
| 174. C32 | #1455 | semidirect |
| 185. C8 | #3711 | semidirect |
| 202. C3 | #68075 | 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 |
| C8×C3⋊(C3⋊C8) | 2 |
| C3×#4455 | 2 |
| #10589079 | 2 |
| #69849 | 3 |
| #68075 | 3 |