Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×#3746 | C2 | semidirect |
| 4. C32×#346 | C2 | semidirect |
| 6. #10589370 | C2 | semidirect |
| 7. #10589369 | C2 | semidirect |
| 20. #63627 | C4 | semidirect |
| 24. C3×#346 | D3 | semidirect |
| 40. #3746 | C2×C4 | semidirect |
| 44. C32×C16 | C2×C4 | semidirect |
| 79. #346 | C3⋊D3 | semidirect |
| 96. C3×C16 | C4×D3 | semidirect |
| 155. C16 | C4×C3⋊D3 | semidirect |
| 167. C32 | #2175 | semidirect |
| 198. C3 | #69077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| C4×#3746 | 2 |
| C4×#3745 | 2 |
| C32×#346 | 2 |
| #10589375 | 2 |
| #10589370 | 2 |
| #10589369 | 2 |
| #69077 | 3 |