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 |
|---|---|---|
| 1. C2×C32×Q32 | C2 | semidirect |
| 3. #10589387 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊C32) | C2 | semidirect |
| 9. C32×Q32 | C22 | semidirect |
| 13. C3⋊(C3⋊C32) | C22 | semidirect |
| 14. C2×C3×Q32 | D3 | semidirect |
| 31. C3×Q32 | C2×D3 | semidirect |
| 45. C2×Q32 | C3⋊D3 | semidirect |
| 67. Q32 | C2×C3⋊D3 | semidirect |
| 81. C2×C32 | SD64 | semidirect |
| 99. C32 | C2×SD64 | semidirect |
| 109. C2×C3 | #4521 | semidirect |
| 118. C3 | C2×#4521 | semidirect |
| 120. C2 | #10589387 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| C2×#63626 | 2 |
| #10589387 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| C2×#4521 | 3 |