Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
493 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 493 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. C3×D3×#107 | C2 | semidirect |
| 3. C2×#63543 | C2 | semidirect |
| 4. #10589358 | C2 | semidirect |
| 5. C3×#4491 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 17. #63807 | C4 | semidirect |
| 29. D3×#107 | D3 | semidirect |
| 38. #4491 | D3 | semidirect |
| 50. #3746 | C2×C4 | semidirect |
| 55. C3×D24 | C2×C4 | semidirect |
| 160. D24 | C4×D3 | semidirect |
| 299. C32 | #2139 | semidirect |
| 346. C3 | #69189 | semidirect |
| 347. C3 | #70598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63807 | 2 |
| C3×D3×#107 | 2 |
| C2×#63543 | 2 |
| #10589358 | 2 |
| C3×#4491 | 2 |
| #10589119 | 2 |
| #10589114 | 2 |
| #70598 | 3 |
| #69189 | 3 |