Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
718 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 247 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 |
|---|---|---|
| 3. C2×#63745 | C2 | direct (N × H) |
| 6. C22×#622 | C4 | semidirect |
| 9. C2×#3787 | C4 | semidirect |
| 11. #63745 | C22 | direct (N × H) |
| 21. C2×#622 | C2×C4 | semidirect |
| 24. #3787 | C2×C4 | semidirect |
| 43. #622 | C22×C4 | semidirect |
| 54. C22×C32 | #106 | semidirect |
| 56. C2×C3⋊D3 | #106 | semidirect |
| 86. C2×C32 | C2×#106 | semidirect |
| 88. C3⋊D3 | C2×#106 | semidirect |
| 114. C32 | C22×#106 | semidirect |
| 139. C22 | #63745 | direct (N × H) |
| 149. C2 | C2×#63745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#157 | 2 |
| C22×#3787 | 2 |
| C2×#63745 | 2 |
| C22×#106 | 9 |