Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2268 conjugacy classes of subgroups; only the 765 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 765 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. #10596290 | C2 | semidirect |
| 3. #10592936 | C2 | semidirect |
| 4. C2×#63660 | C2 | semidirect |
| 13. C2×#3748 | C22 | semidirect |
| 14. #63663 | C22 | semidirect |
| 15. #63660 | C22 | semidirect |
| 150. C32 | #2888 | semidirect |
| 180. C3 | #84100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×H(5,𝔽2) | 2 |
| #10596290 | 2 |
| #10592936 | 2 |
| C2×#63660 | 2 |
| #84100 | 3 |