Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#64128 | C2 | semidirect |
| 2. C2×C32×SD32 | C2 | semidirect |
| 3. #10592856 | C2 | semidirect |
| 4. C2×#63653 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 6. #10589375 | C2 | semidirect |
| 7. #10589373 | C2 | semidirect |
| 25. C2×C3×SD32 | D3 | semidirect |
| 41. C32×Q16 | D4 | semidirect |
| 50. #3745 | D4 | semidirect |
| 93. C2×SD32 | C3⋊D3 | semidirect |
| 109. C3×Q16 | #67 | semidirect |
| 190. Q16 | #638 | semidirect |
| 219. C32 | #2186 | semidirect |
| 262. C3 | #71484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64128 | 2 |
| C2×C32×SD32 | 2 |
| #10592856 | 2 |
| C2×#63653 | 2 |
| #10589430 | 2 |
| #10589375 | 2 |
| #10589373 | 2 |
| #71484 | 3 |