Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1188 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 195 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×#100 | C2 | semidirect |
| 3. C2×#63660 | C2 | semidirect |
| 4. C2×#63650 | C2 | semidirect |
| 5. C2×#63650 | C2 | semidirect |
| 6. #10592817 | C2 | semidirect |
| 7. M16×C3⋊Dic3 | C2 | semidirect |
| 28. C2×C3×#100 | D3 | semidirect |
| 56. C32×M16 | D4 | semidirect |
| 65. #3748 | D4 | semidirect |
| 124. C2×#100 | C3⋊D3 | semidirect |
| 148. C3×M16 | #67 | semidirect |
| 177. C3⋊Dic3 | #100 | semidirect |
| 260. M16 | #638 | semidirect |
| 286. C32 | #1965 | semidirect |
| 343. C3 | #70064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64149 | 2 |
| C2×C32×#100 | 2 |
| C2×#63660 | 2 |
| C2×#63650 | 2 |
| #10592817 | 2 |
| M16×C3⋊Dic3 | 2 |
| #70064 | 3 |