Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
497 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 497 conjugacy classes of subgroups — too many to draw. Only its 114 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×#798 | C2 | semidirect |
| 3. D3×#818 | C2 | semidirect |
| 4. #10589375 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 7. #10589116 | C2 | semidirect |
| 17. #63808 | C4 | semidirect |
| 28. C2×#798 | D3 | semidirect |
| 37. #4503 | D3 | semidirect |
| 50. #3745 | C2×C4 | semidirect |
| 54. C3×Dic12 | C2×C4 | semidirect |
| 154. Dic12 | C4×D3 | semidirect |
| 301. C32 | #2139 | semidirect |
| 349. C3 | #69221 | semidirect |
| 350. C3 | #71439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63808 | 2 |
| C2×C3×#798 | 2 |
| D3×#818 | 2 |
| #10589375 | 2 |
| C3×#4503 | 2 |
| #10589118 | 2 |
| #10589116 | 2 |
| #71439 | 3 |
| #69221 | 3 |