Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 561 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 561 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. #63630 | C4 | direct (N × H) |
| 10. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 36. C3⋊(C3⋊C8) | C42 | semidirect |
| 52. C32×C4 | #97 | semidirect |
| 83. C3×C4 | #803 | semidirect |
| 85. C32 | C4×#97 | semidirect |
| 101. C4 | #63630 | direct (N × H) |
| 103. C3 | C4×#803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C43 | 2 |
| C2×#63630 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C4×#803 | 3 |