Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
485 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 485 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×D3×C16 | C2 | semidirect |
| 3. #10590707 | C2 | semidirect |
| 4. #10589369 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 17. #63807 | C4 | semidirect |
| 28. C2×D3×C16 | D3 | semidirect |
| 33. #4509 | D3 | semidirect |
| 296. C32 | #2138 | semidirect |
| 342. C3 | #69188 | semidirect |
| 343. C3 | #71412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63807 | 2 |
| C2×C3×D3×C16 | 2 |
| #10590707 | 2 |
| #10589369 | 2 |
| C3×#4509 | 2 |
| #10589119 | 2 |
| #10589115 | 2 |
| #71412 | 3 |
| #69188 | 3 |