Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 120 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. C3×#4680 | C2 | semidirect |
| 4. #10590309 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 24. #4680 | D3 | semidirect |
| 70. C32×C8 | SD16 | semidirect |
| 71. C3⋊(C3⋊C8) | SD16 | semidirect |
| 141. C3×C8 | #214 | semidirect |
| 142. C3×C8 | #215 | semidirect |
| 178. C32 | #1705 | semidirect |
| 189. C8 | #3715 | semidirect |
| 206. C3 | #71254 | semidirect |
| 207. C3 | #71332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4693 | 2 |
| C3×#4680 | 2 |
| #10590375 | 2 |
| #10590309 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71332 | 3 |
| #71254 | 3 |