Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 72 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×#63467 | C2 | semidirect |
| 2. C9×#466 | C2 | semidirect |
| 3. C2×#63386 | C2 | semidirect |
| 4. C2×#63385 | C2 | semidirect |
| 5. #10588226 | C2 | semidirect |
| 6. #10588169 | C2 | semidirect |
| 7. #10588168 | C2 | semidirect |
| 49. D72 | D4 | semidirect |
| 52. Dic36 | D4 | semidirect |
| 95. #466 | D9 | semidirect |
| 219. C9 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63467 | 2 |
| C9×#466 | 2 |
| C2×#63386 | 2 |
| C2×#63385 | 2 |
| #10588226 | 2 |
| #10588169 | 2 |
| #10588168 | 2 |
| #71076 | 3 |