Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
469 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 469 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 4. #10589430 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 14. C3×D3×Q16 | C4 | semidirect |
| 36. #4564 | D3 | semidirect |
| 75. D3×Q16 | Dic3 | semidirect |
| 289. C32 | #2141 | semidirect |
| 331. C3 | #69222 | semidirect |
| 332. C3 | #72061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q16 | 2 |
| #10590707 | 2 |
| C2×#63543 | 2 |
| #10589430 | 2 |
| C3×#4564 | 2 |
| #10589118 | 2 |
| #10589117 | 2 |
| #72061 | 3 |
| #69222 | 3 |