Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
672 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 209 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. #10592393 | C2 | semidirect |
| 3. #10592392 | C2 | semidirect |
| 4. #10592381 | C2 | semidirect |
| 5. C32×C82 | C2 | semidirect |
| 20. C3×C82 | D3 | semidirect |
| 53. C32×C8 | D8 | semidirect |
| 54. C32×C8 | SD16 | semidirect |
| 59. C82 | C3⋊D3 | semidirect |
| 99. C3×C8 | #204 | semidirect |
| 100. C3×C8 | D24 | semidirect |
| 125. C32 | #1706 | semidirect |
| 136. C8 | #3744 | semidirect |
| 137. C8 | #3745 | semidirect |
| 150. C3 | #68058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592394 | 2 |
| #10592393 | 2 |
| #10592392 | 2 |
| #10592381 | 2 |
| C32×C82 | 2 |
| #68058 | 3 |