Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
798 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 175 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. #10592936 | C2 | semidirect |
| 3. C2×#63664 | C2 | semidirect |
| 4. #10592817 | C2 | semidirect |
| 5. #10589426 | C2 | semidirect |
| 194. C32 | #2050 | semidirect |
| 231. C3 | #72117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#575 | 2 |
| #10592936 | 2 |
| C2×#63664 | 2 |
| #10592817 | 2 |
| #10589426 | 2 |
| #72117 | 3 |