Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
418 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 3. C32×#330 | C2 | semidirect |
| 4. C3×#4543 | C2 | semidirect |
| 5. C3×#4465 | C2 | semidirect |
| 7. #68369 | C3 | direct (N × H) |
| 26. C3×#330 | D3 | semidirect |
| 27. C3×#330 | C2×C3 | semidirect |
| 28. #4543 | C2×C3 | semidirect |
| 29. #4465 | C2×C3 | semidirect |
| 86. #330 | C3×D3 | semidirect |
| 209. C32 | #1537 | semidirect |
| 240. C3 | #68369 | direct (N × H) |
| 241. C3 | C3×#1537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5688 | 2 |
| C3×#4705 | 2 |
| C32×#330 | 2 |
| C3×#4543 | 2 |
| C3×#4465 | 2 |
| C3×#1537 | 3 |
| #68369 | 3 |