Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
653 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 653 conjugacy classes of subgroups — too many to draw. Only its 148 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. C3×#5106 | C2 | semidirect |
| 4. #10589157 | C2 | semidirect |
| 11. C2×#3743 | C4 | semidirect |
| 12. C2×C8×C3⋊D3 | C4 | semidirect |
| 20. #5106 | D3 | semidirect |
| 237. C32 | #1812 | semidirect |
| 275. C3 | #70664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64110 | 2 |
| C3×#5106 | 2 |
| #10591232 | 2 |
| #10589157 | 2 |
| #70664 | 3 |