Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
387 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 387 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 |
|---|---|---|
| 2. #10588920 | C2 | semidirect |
| 3. #10588222 | C2 | semidirect |
| 4. #10588218 | C2 | semidirect |
| 6. C2×C9×#41 | C4 | semidirect |
| 8. C9×C4⋊Q8 | C4 | semidirect |
| 10. C9×#124 | C4 | semidirect |
| 14. C2×C42×C9 | C4 | semidirect |
| 126. C2×#41 | Dic9 | semidirect |
| 128. C4⋊Q8 | Dic9 | semidirect |
| 130. #124 | Dic9 | semidirect |
| 135. C2×C42 | Dic9 | semidirect |
| 206. C9 | #2126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#532 | 2 |
| #10588920 | 2 |
| #10588222 | 2 |
| #10588218 | 2 |
| #71819 | 3 |