Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
490 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 66 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×#63771 | C2 | semidirect |
| 3. C2×#63764 | C2 | semidirect |
| 4. #10590198 | C2 | direct (N × H) |
| 17. #63771 | C22 | semidirect |
| 19. #63764 | C22 | semidirect |
| 150. C2×C32 | #359 | semidirect |
| 191. C32 | C2×#359 | semidirect |
| 234. C2 | #10590198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64128 | 2 |
| C2×#63771 | 2 |
| C2×#63764 | 2 |
| #10590198 | 2 |
| C2×#359 | 9 |