Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1682 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1682 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#3788 | C2 | semidirect |
| 3. C22×#3787 | C2 | semidirect |
| 4. C2×C22⋊#622 | C2 | semidirect |
| 5. #10593823 | C2 | direct (N × H) |
| 18. C2×#3788 | C22 | semidirect |
| 20. C2×#3787 | C22 | semidirect |
| 21. C22⋊#622 | C22 | semidirect |
| 169. C2×C32 | #408 | semidirect |
| 215. C32 | C2×#408 | semidirect |
| 264. C2 | #10593823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3830 | 2 |
| C22×#3788 | 2 |
| C22×#3787 | 2 |
| C2×C22⋊#622 | 2 |
| #10593823 | 2 |
| C2×#408 | 9 |