Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1026 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 1. C22×#3756 | C2 | semidirect |
| 4. C2×C32×#101 | C2 | semidirect |
| 5. C2×#63651 | C2 | semidirect |
| 7. #10589424 | C2 | semidirect |
| 33. C2×C3×#101 | D3 | semidirect |
| 138. C2×#101 | C3⋊D3 | semidirect |
| 308. C32 | #2020 | semidirect |
| 362. C3 | #70125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3756 | 2 |
| C2×#64151 | 2 |
| C2×#64118 | 2 |
| C2×C32×#101 | 2 |
| C2×#63651 | 2 |
| #10592828 | 2 |
| #10589424 | 2 |
| #70125 | 3 |