Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1146 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 191 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×C32×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×#64158 | C2 | semidirect |
| 3. C22×#3753 | C2 | semidirect |
| 4. #10592933 | C2 | semidirect |
| 5. C2×#63660 | C2 | semidirect |
| 6. C2×#63650 | C2 | semidirect |
| 7. #10589424 | C2 | semidirect |
| 30. C2×C3×AGL(1,ℤ/8) | D3 | semidirect |
| 137. C2×AGL(1,ℤ/8) | C3⋊D3 | semidirect |
| 326. C32 | #2018 | semidirect |
| 390. C3 | #72095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×AGL(1,ℤ/8) | 2 |
| C2×#64158 | 2 |
| C22×#3753 | 2 |
| #10592933 | 2 |
| C2×#63660 | 2 |
| C2×#63650 | 2 |
| #10589424 | 2 |
| #72095 | 3 |