Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
612 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 121 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. #10592772 | C2 | semidirect |
| 2. #10592771 | C2 | semidirect |
| 3. #10592542 | C2 | semidirect |
| 4. #10592533 | C2 | semidirect |
| 5. C32×#331 | C2 | semidirect |
| 6. #10589351 | C2 | semidirect |
| 7. #10589345 | C2 | semidirect |
| 28. C3×#331 | D3 | semidirect |
| 86. C4⋊(C3⋊D3) | D8 | semidirect |
| 93. C3⋊(C3⋊C8) | D8 | semidirect |
| 100. #331 | C3⋊D3 | semidirect |
| 222. C32 | #1667 | semidirect |
| 271. C3 | #68395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592772 | 2 |
| #10592771 | 2 |
| #10592542 | 2 |
| #10592533 | 2 |
| C32×#331 | 2 |
| #10589351 | 2 |
| #10589345 | 2 |
| #68395 | 3 |