Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
499 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 499 conjugacy classes of subgroups — too many to draw. Only its 152 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. C3×#4454 | C2 | semidirect |
| 4. #10589079 | C2 | semidirect |
| 5. C3⋊C82 | C2 | semidirect |
| 22. #4454 | D3 | semidirect |
| 62. C3⋊(C3⋊C8) | M16 | semidirect |
| 64. C3×C3⋊C8 | M16 | semidirect |
| 134. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 166. C32 | #1455 | semidirect |
| 193. C3 | #68075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3743 | 2 |
| C4×#3712 | 2 |
| C3×#4454 | 2 |
| #10589079 | 2 |
| C3⋊C82 | 2 |
| #68075 | 3 |