Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
726 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 165 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×#492 | C2 | semidirect |
| 2. #10592787 | C2 | semidirect |
| 3. #10592772 | C2 | semidirect |
| 4. #10592394 | C2 | semidirect |
| 5. #10589321 | C2 | semidirect |
| 16. C3×#492 | D3 | semidirect |
| 55. C32×C8 | D8 | semidirect |
| 59. #492 | C3⋊D3 | semidirect |
| 104. C3×C8 | #213 | semidirect |
| 132. C32 | #1721 | semidirect |
| 145. C8 | #3753 | semidirect |
| 159. C3 | #71262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| #10592787 | 2 |
| #10592772 | 2 |
| #10592394 | 2 |
| #10589321 | 2 |
| #71262 | 3 |