Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
517 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 517 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×#4695 | C2 | semidirect |
| 2. C3×#4695 | C2 | semidirect |
| 3. C3×#4694 | C2 | semidirect |
| 4. C3×#4693 | C2 | semidirect |
| 5. C32×#322 | C2 | semidirect |
| 7. #68094 | C3 | direct (N × H) |
| 21. #4695 | C2×C3 | semidirect |
| 22. #4695 | C2×C3 | semidirect |
| 23. #4694 | C2×C3 | semidirect |
| 24. #4693 | C2×C3 | semidirect |
| 26. C3×#322 | D3 | semidirect |
| 27. C3×#322 | C2×C3 | semidirect |
| 74. C32×C8 | D8 | semidirect |
| 79. #322 | C3×D3 | semidirect |
| 155. C3×C8 | D24 | semidirect |
| 156. C3×C8 | C3×D8 | semidirect |
| 195. C32 | #1721 | semidirect |
| 208. C8 | C3×D24 | semidirect |
| 229. C3 | #68094 | direct (N × H) |
| 230. C3 | C3×#1721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| C3×#4694 | 2 |
| C3×#4693 | 2 |
| C32×#322 | 2 |
| C3×#1721 | 3 |
| #68094 | 3 |