Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
971 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 971 conjugacy classes of subgroups — too many to draw. Only its 214 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×#5577 | C2 | semidirect |
| 2. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. #10590352 | C2 | semidirect |
| 4. #10590347 | C2 | semidirect |
| 5. C4×#3713 | C2 | semidirect |
| 19. #5577 | D3 | semidirect |
| 61. C32×Q8 | D8 | semidirect |
| 72. C3⋊(C3⋊C8) | #41 | semidirect |
| 127. C3×Q8 | #213 | semidirect |
| 186. C32 | #3391 | semidirect |
| 188. Q8 | #3713 | semidirect |
| 218. C3 | #83582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5577 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10590352 | 2 |
| #10590347 | 2 |
| C4×#3713 | 2 |
| #83582 | 3 |