Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
938 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 258 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×#63768 | C2 | direct (N × H) |
| 8. C22×C32×C8 | C4 | semidirect |
| 9. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 10. C2×C8×C3⋊D3 | C4 | semidirect |
| 12. #63768 | C22 | direct (N × H) |
| 25. C2×C32×C8 | C2×C4 | semidirect |
| 26. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 27. C8×C3⋊D3 | C2×C4 | semidirect |
| 50. C32×C8 | C22×C4 | semidirect |
| 51. C3⋊(C3⋊C8) | C22×C4 | semidirect |
| 66. C22×C32 | #106 | semidirect |
| 68. C2×C3⋊D3 | #106 | semidirect |
| 82. C22×C8 | #157 | semidirect |
| 101. C2×C32 | C2×#106 | semidirect |
| 103. C3⋊D3 | C2×#106 | semidirect |
| 117. C2×C8 | C2×#157 | semidirect |
| 130. C32 | C22×#106 | semidirect |
| 147. C8 | C22×#157 | semidirect |
| 156. C22 | #63768 | direct (N × H) |
| 166. C2 | C2×#63768 | 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×C8×C3⋊D3 | 2 |
| C2×#63768 | 2 |
| C22×#106 | 9 |