Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
573 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 104 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×C9×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×#63512 | C2 | semidirect |
| 3. C22×#3673 | C2 | semidirect |
| 4. #10588912 | C2 | semidirect |
| 5. C2×#63391 | C2 | semidirect |
| 6. C2×#63383 | C2 | semidirect |
| 7. #10588231 | C2 | semidirect |
| 137. C2×AGL(1,ℤ/8) | D9 | semidirect |
| 326. C9 | #2018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×AGL(1,ℤ/8) | 2 |
| C2×#63512 | 2 |
| C22×#3673 | 2 |
| #10588912 | 2 |
| C2×#63391 | 2 |
| C2×#63383 | 2 |
| #10588231 | 2 |
| #72095 | 3 |