Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2394 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 2394 conjugacy classes of subgroups — too many to draw. Only its 770 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×#64289 | C2 | direct (N × H) |
| 3. C22×#3788 | C2 | semidirect |
| 4. C22×#3787 | C2 | semidirect |
| 12. #64289 | C22 | direct (N × H) |
| 13. C2×#3788 | C22 | semidirect |
| 14. C2×#3787 | C22 | semidirect |
| 27. #3788 | C23 | semidirect |
| 28. #3787 | C23 | semidirect |
| 60. C22×C32 | #131 | semidirect |
| 87. C2×C32 | C2×#131 | semidirect |
| 110. C32 | C22×#131 | semidirect |
| 128. C22 | #64289 | direct (N × H) |
| 135. C2 | C2×#64289 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| C2×#64289 | 2 |
| C22×#3788 | 2 |
| C22×#3787 | 2 |
| C22×#131 | 9 |