Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 66 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. C9×#473 | C2 | semidirect |
| 3. C2×#63388 | C2 | semidirect |
| 4. #10588859 | C2 | semidirect |
| 5. #10588238 | C2 | semidirect |
| 6. #10588174 | C2 | semidirect |
| 7. #10588173 | C2 | semidirect |
| 104. #473 | D9 | semidirect |
| 224. C9 | #2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589855 | 2 |
| C9×#473 | 2 |
| C2×#63388 | 2 |
| #10588859 | 2 |
| #10588238 | 2 |
| #10588174 | 2 |
| #10588173 | 2 |
| #71099 | 3 |