Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1128 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 269 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×C32×#106 | C2 | semidirect |
| 3. C2×#63642 | C2 | semidirect |
| 4. #10592687 | C2 | semidirect |
| 5. C2×#63636 | C2 | semidirect |
| 15. C2×#3745 | C4 | semidirect |
| 20. C2×C3×#106 | D3 | semidirect |
| 79. C32×C8 | C22⋊C4 | semidirect |
| 82. C2×#106 | C3⋊D3 | semidirect |
| 155. C3×C8 | (C2×D3)⋊C4 | semidirect |
| 199. C32 | #1972 | semidirect |
| 221. C8 | #3752 | semidirect |
| 242. C3 | #70576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| C2×C32×#106 | 2 |
| C2×#63642 | 2 |
| #10592687 | 2 |
| C2×#63636 | 2 |
| #70576 | 3 |