Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
373 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 373 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 5. #68064 | C3 | direct (N × H) |
| 105. C32 | #1710 | semidirect |
| 123. C3 | #68064 | direct (N × H) |
| 124. C3 | C3×#1710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4682 | 2 |
| C3×#4681 | 2 |
| C32×C82 | 2 |
| C3×#1710 | 3 |
| #68064 | 3 |