Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2316 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 2316 conjugacy classes of subgroups — too many to draw. Only its 381 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. C32×#585 | C2 | semidirect |
| 2. #10596301 | C2 | semidirect |
| 3. #10592943 | C2 | semidirect |
| 4. #10592939 | C2 | semidirect |
| 11. C22×C4⋊(C3⋊D3) | C22 | semidirect |
| 14. #64146 | C22 | semidirect |
| 16. #64135 | C22 | semidirect |
| 17. #63661 | C22 | semidirect |
| 18. C3×#585 | D3 | semidirect |
| 29. C2×C32×Q8 | D4 | semidirect |
| 32. C2×C32×D4 | D4 | semidirect |
| 35. C22×C32×C4 | D4 | semidirect |
| 77. #585 | C3⋊D3 | semidirect |
| 88. C2×C3×Q8 | #67 | semidirect |
| 91. C2×C3×D4 | #67 | semidirect |
| 94. C22×C3×C4 | #67 | semidirect |
| 157. C2×Q8 | #638 | semidirect |
| 163. C2×D4 | #638 | semidirect |
| 166. C22×C4 | #638 | semidirect |
| 183. C32 | #3027 | semidirect |
| 219. C3 | #84126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#585 | 2 |
| #10596301 | 2 |
| #10592943 | 2 |
| #10592939 | 2 |
| #84126 | 3 |