Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
442 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. C32×C4×C8 | C4 | semidirect |
| 10. C8×C3⋊Dic3 | C4 | semidirect |
| 11. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 41. C32×C8 | C4⋊C4 | semidirect |
| 42. C3⋊(C3⋊C8) | C4⋊C4 | semidirect |
| 60. C32×C4 | #106 | semidirect |
| 62. C3⋊Dic3 | #106 | semidirect |
| 71. C4×C8 | #157 | semidirect |
| 106. C32 | #1844 | semidirect |
| 118. C8 | C4⋊#157 | semidirect |
| 130. C4 | #63768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63768 | 2 |
| #10593735 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #1844 | 9 |