Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
634 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 202 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×#63773 | C2 | semidirect |
| 3. C22×#3708 | C2 | semidirect |
| 4. #10593772 | C2 | direct (N × H) |
| 5. C2×#63765 | C2 | semidirect |
| 6. C2×#63764 | C2 | semidirect |
| 14. #63773 | C22 | semidirect |
| 18. C2×#3708 | C22 | semidirect |
| 19. #63765 | C22 | semidirect |
| 20. #63764 | C22 | semidirect |
| 127. C2×C32 | #504 | semidirect |
| 158. C32 | C2×#504 | semidirect |
| 191. C2 | #10593772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64116 | 2 |
| C2×#63773 | 2 |
| C22×#3708 | 2 |
| #10593772 | 2 |
| C2×#63765 | 2 |
| C2×#63764 | 2 |
| C2×#504 | 9 |