Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
518 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 518 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 |
|---|---|---|
| 2. C2×#64218 | C2 | direct (N × H) |
| 3. C22×#3771 | C2 | semidirect |
| 9. #64218 | C22 | direct (N × H) |
| 10. C2×#3771 | C22 | semidirect |
| 21. #3771 | C23 | semidirect |
| 44. C22×C32 | M32 | semidirect |
| 66. C2×C32 | C2×M32 | semidirect |
| 86. C32 | C22×M32 | semidirect |
| 102. C22 | #64218 | direct (N × H) |
| 110. C2 | C2×#64218 | 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×#64218 | 2 |
| C22×#3771 | 2 |
| C22×M32 | 9 |