Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
621 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 621 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. C2×C3×#812 | C2 | semidirect |
| 3. #10589110 | C2 | direct (N × H) |
| 13. C3×#812 | C22 | semidirect |
| 18. C2×#812 | D3 | semidirect |
| 60. #812 | C2×D3 | semidirect |
| 197. C2×C32 | #349 | semidirect |
| 245. C32 | C2×#349 | semidirect |
| 273. C2×C3 | #4514 | semidirect |
| 291. C3 | C2×#4514 | semidirect |
| 295. C2 | #10589110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3743 | 2 |
| C2×C3×#812 | 2 |
| #10589110 | 2 |
| C2×#4514 | 3 |