Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 138 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. C3×#4699 | C2 | semidirect |
| 4. C3×#4682 | C2 | semidirect |
| 5. C32×#322 | C2 | semidirect |
| 7. #68098 | C3 | direct (N × H) |
| 21. #4699 | C2×C3 | semidirect |
| 24. #4682 | C2×C3 | semidirect |
| 26. C3×#322 | D3 | semidirect |
| 27. C3×#322 | C2×C3 | semidirect |
| 76. #322 | C3×D3 | semidirect |
| 178. C32 | #1722 | semidirect |
| 206. C3 | #68098 | direct (N × H) |
| 207. C3 | C3×#1722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4694 | 2 |
| C3×#4693 | 2 |
| C3×#4682 | 2 |
| C32×#322 | 2 |
| C3×#1722 | 3 |
| #68098 | 3 |