Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
545 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 545 conjugacy classes of subgroups — too many to draw. Only its 92 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. C2×C3×#827 | C2 | semidirect |
| 3. #10590851 | C2 | semidirect |
| 4. C2×#63547 | C2 | semidirect |
| 5. #10589428 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 15. C2×C3×Dic12 | C22 | semidirect |
| 19. #63645 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 22. C2×C3×C3⋊C16 | C22 | semidirect |
| 31. C2×#827 | D3 | semidirect |
| 81. C2×Dic12 | C2×D3 | semidirect |
| 97. C2×C3⋊C16 | C2×D3 | semidirect |
| 191. C2×C3×D3 | SD32 | semidirect |
| 318. C2×D3 | #827 | semidirect |
| 332. C32 | #2187 | semidirect |
| 388. C3 | #71485 | semidirect |
| 389. C3 | #72036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×D8 | 2 |
| C2×C3×#827 | 2 |
| #10590851 | 2 |
| C2×#63547 | 2 |
| #10589428 | 2 |
| #10589115 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #72036 | 3 |
| #71485 | 3 |