Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
846 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 187 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. #10592933 | C2 | semidirect |
| 3. #10592931 | C2 | semidirect |
| 4. C2×#63660 | C2 | semidirect |
| 5. C2×#63659 | C2 | semidirect |
| 6. C2×#63649 | C2 | semidirect |
| 7. #10589420 | C2 | semidirect |
| 283. C32 | #2051 | semidirect |
| 342. C3 | #72093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×AGL(1,ℤ/8) | 2 |
| #10592933 | 2 |
| #10592931 | 2 |
| C2×#63660 | 2 |
| C2×#63659 | 2 |
| C2×#63649 | 2 |
| #10589420 | 2 |
| #72093 | 3 |