Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
876 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 191 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. C32×#408 | C2 | semidirect |
| 3. C2×#63664 | C2 | semidirect |
| 4. C2×#63652 | C2 | semidirect |
| 5. C2×#63649 | C2 | semidirect |
| 6. #10592809 | C2 | semidirect |
| 7. C2×#63642 | C2 | semidirect |
| 15. C2×#3756 | C4 | semidirect |
| 16. C2×#3755 | C4 | semidirect |
| 17. C2×#3754 | C4 | semidirect |
| 18. C2×#3753 | C4 | semidirect |
| 29. C3×#408 | D3 | semidirect |
| 131. #408 | C3⋊D3 | semidirect |
| 296. C32 | #1975 | semidirect |
| 352. C3 | #70000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64159 | 2 |
| C32×#408 | 2 |
| C2×#63664 | 2 |
| C2×#63652 | 2 |
| C2×#63649 | 2 |
| #10592809 | 2 |
| C2×#63642 | 2 |
| #70000 | 3 |