Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1609 conjugacy classes of subgroups; only the 756 normal subgroups are shown.
This group has 1609 conjugacy classes of subgroups — too many to draw. Only its 756 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×#63555 | C2 | direct (N × H) |
| 9. C22×C3×C3⋊C8 | C4 | semidirect |
| 11. #63555 | C22 | direct (N × H) |
| 25. C2×C3×C3⋊C8 | C2×C4 | semidirect |
| 38. C22×C3⋊C8 | Dic3 | semidirect |
| 50. C3×C3⋊C8 | C22×C4 | semidirect |
| 73. C2×C3⋊C8 | C2×Dic3 | semidirect |
| 75. C22×C32 | #97 | semidirect |
| 109. C3⋊C8 | C22×Dic3 | semidirect |
| 110. C2×C32 | C2×#97 | semidirect |
| 127. C22×C3 | #815 | semidirect |
| 138. C32 | C22×#97 | semidirect |
| 152. C2×C3 | C2×#815 | semidirect |
| 155. C22 | #63555 | direct (N × H) |
| 163. C3 | C22×#815 | semidirect |
| 164. C2 | C2×#63555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊Dic3 | 2 |
| C23×C3×C3⋊C8 | 2 |
| C2×#63555 | 2 |
| C22×#815 | 3 |