Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
355 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 4. C3⋊#1309 | C3 | direct (N × H) |
| 165. C32 | #1309 | semidirect |
| 196. C3 | C3⋊#1309 | direct (N × H) |
| 197. C3 | C3×#1309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#423 | 2 |
| C3×#4924 | 2 |
| C3×#1309 | 3 |
| C3⋊#1309 | 3 |