Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1109 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1109 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×#64116 | C2 | semidirect |
| 2. C2×#63830 | C2 | semidirect |
| 3. C22×#3713 | C2 | semidirect |
| 4. C2×C3×#823 | C2 | semidirect |
| 5. C2×#63578 | C2 | semidirect |
| 6. #10590988 | C2 | direct (N × H) |
| 13. #64116 | C22 | semidirect |
| 18. #63830 | C22 | semidirect |
| 24. C2×#3713 | C22 | semidirect |
| 25. C3×#823 | C22 | semidirect |
| 26. #63578 | C22 | semidirect |
| 33. C2×#823 | D3 | semidirect |
| 100. #823 | C2×D3 | semidirect |
| 293. C2×C32 | #472 | semidirect |
| 359. C32 | C2×#472 | semidirect |
| 396. C2×C3 | #4749 | semidirect |
| 417. C3 | C2×#4749 | semidirect |
| 422. C2 | #10590988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64116 | 2 |
| C2×#63830 | 2 |
| C22×#3713 | 2 |
| C2×C3×#823 | 2 |
| C2×#63578 | 2 |
| #10590988 | 2 |
| C2×#4749 | 3 |