Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
423 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 423 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10588916 | C2 | semidirect |
| 3. #10588912 | C2 | semidirect |
| 4. C2×#63392 | C2 | semidirect |
| 5. C2×#63391 | C2 | semidirect |
| 6. C2×#63381 | C2 | semidirect |
| 7. #10588234 | C2 | semidirect |
| 283. C9 | #2051 | 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 |
| #10588916 | 2 |
| #10588912 | 2 |
| C2×#63392 | 2 |
| C2×#63391 | 2 |
| C2×#63381 | 2 |
| #10588234 | 2 |
| #72093 | 3 |