Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2474 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 2474 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×C22⋊#157 | C2 | semidirect |
| 3. C2×#63774 | C2 | direct (N × H) |
| 4. C24×C3⋊D3 | C4 | semidirect |
| 7. C23×C32×C4 | C4 | semidirect |
| 10. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 13. C2×C22⋊#157 | C22 | semidirect |
| 14. #63774 | C22 | direct (N × H) |
| 22. C23×C3⋊D3 | C2×C4 | semidirect |
| 30. C22×C32×C4 | C2×C4 | semidirect |
| 35. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 38. C22⋊#157 | C23 | semidirect |
| 63. C22×C3⋊D3 | C22×C4 | semidirect |
| 71. C2×C32×C4 | C22×C4 | semidirect |
| 98. C22×C32 | #99 | semidirect |
| 123. C23×C4 | #157 | semidirect |
| 154. C2×C32 | C2×#99 | semidirect |
| 179. C22×C4 | C2×#157 | semidirect |
| 201. C32 | C22×#99 | semidirect |
| 228. C2×C4 | C22×#157 | semidirect |
| 250. C22 | #63774 | direct (N × H) |
| 262. C2 | C2×#63774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊(C3⋊D3) | 2 |
| C22×C22⋊#157 | 2 |
| C2×#63774 | 2 |
| C22×#99 | 9 |