Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
842 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. #10593511 | C2 | direct (N × H) |
| 4. C2×#63743 | C2 | semidirect |
| 5. C2×#63742 | C2 | semidirect |
| 7. C22×#622 | C4 | semidirect |
| 16. #63743 | C22 | semidirect |
| 17. #63742 | C22 | semidirect |
| 29. C2×#622 | C2×C4 | semidirect |
| 121. C2×C32 | #427 | semidirect |
| 153. C32 | C2×#427 | semidirect |
| 188. C2 | #10593511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#622 | 2 |
| C2×#63957 | 2 |
| #10593511 | 2 |
| C2×#63743 | 2 |
| C2×#63742 | 2 |
| C2×#427 | 9 |