Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#63628 | C2 | semidirect |
| 3. #10589386 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊C32) | C2 | semidirect |
| 12. #63628 | C22 | semidirect |
| 13. C3⋊(C3⋊C32) | C22 | semidirect |
| 82. C2×C32 | SD64 | semidirect |
| 99. C32 | C2×SD64 | semidirect |
| 110. C2×C3 | #4520 | semidirect |
| 118. C3 | C2×#4520 | semidirect |
| 120. C2 | #10589386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C2×#63628 | 2 |
| #10589386 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| C2×#4520 | 3 |