Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1110 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64160 | C2 | semidirect |
| 3. C2×#63664 | C2 | semidirect |
| 4. #10592672 | C2 | semidirect |
| 5. #10589396 | C2 | semidirect |
| 42. C2×#634 | D4 | semidirect |
| 50. #3748 | D4 | semidirect |
| 226. C32 | #2007 | semidirect |
| 274. C3 | #71881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#537 | 2 |
| C2×#64160 | 2 |
| C2×#63664 | 2 |
| #10592672 | 2 |
| #10589396 | 2 |
| #71881 | 3 |