Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1341 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 1341 conjugacy classes of subgroups — too many to draw. Only its 153 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×#63690 | C2 | direct (N × H) |
| 3. C22×#3688 | C2 | semidirect |
| 8. #63690 | C22 | direct (N × H) |
| 9. C2×#3688 | C22 | semidirect |
| 22. #3688 | C23 | semidirect |
| 176. C22 | #63690 | direct (N × H) |
| 184. C2 | C2×#63690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41⋊C9 | 2 |
| C2×#63690 | 2 |
| C22×#3688 | 2 |
| C22×#951 | 3 |
| C22×Dic18 | 4 |