Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
493 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 493 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 |
|---|---|---|
| 2. D3×#818 | C2 | semidirect |
| 3. C2×#63543 | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 14. C3×#919 | C4 | semidirect |
| 34. #4564 | D3 | semidirect |
| 48. C32×Q16 | C2×C4 | semidirect |
| 55. C3×D24 | C2×C4 | semidirect |
| 75. #919 | Dic3 | semidirect |
| 140. C3×Q16 | C4×D3 | semidirect |
| 141. C3×Q16 | C2×Dic3 | semidirect |
| 161. D24 | C2×Dic3 | semidirect |
| 255. Q16 | D3×Dic3 | semidirect |
| 299. C32 | #2139 | semidirect |
| 346. C3 | #69221 | semidirect |
| 347. C3 | #72078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#919 | 2 |
| D3×#818 | 2 |
| C2×#63543 | 2 |
| #10589430 | 2 |
| C3×#4564 | 2 |
| #10589115 | 2 |
| #10589114 | 2 |
| #72078 | 3 |
| #69221 | 3 |