Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
337 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5197 | C2 | semidirect |
| 3. #10590771 | C2 | semidirect |
| 4. #10589432 | C2 | semidirect |
| 5. #10589137 | C2 | semidirect |
| 6. #10589126 | C2 | semidirect |
| 7. #10589105 | C2 | semidirect |
| 17. C3×#828 | C4 | semidirect |
| 18. C3×#826 | C4 | semidirect |
| 25. #5197 | D3 | semidirect |
| 41. C32×Q16 | C2×C4 | semidirect |
| 43. C32×D8 | C2×C4 | semidirect |
| 55. C3×C3⋊C16 | C2×C4 | semidirect |
| 74. #828 | Dic3 | semidirect |
| 75. #826 | Dic3 | semidirect |
| 116. C3×Q16 | C4×D3 | semidirect |
| 117. C3×Q16 | C2×Dic3 | semidirect |
| 124. C3×D8 | C4×D3 | semidirect |
| 125. C3×D8 | C2×Dic3 | semidirect |
| 150. C3⋊C16 | C2×Dic3 | semidirect |
| 219. Q16 | D3×Dic3 | semidirect |
| 223. D8 | D3×Dic3 | semidirect |
| 260. C32 | AGL(1,ℤ/16) | semidirect |
| 298. C3 | #70929 | semidirect |
| 299. C3 | #71515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5197 | 2 |
| C3×#5193 | 2 |
| #10590771 | 2 |
| #10589432 | 2 |
| #10589137 | 2 |
| #10589126 | 2 |
| #10589105 | 2 |
| #71515 | 3 |
| #70929 | 3 |