Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 4. M16×Dic9 | C2 | semidirect |
| 5. #10588800 | C2 | semidirect |
| 6. #10588235 | C2 | semidirect |
| 7. #10588232 | C2 | semidirect |
| 16. C9×#101 | C4 | semidirect |
| 17. C9×#100 | C4 | semidirect |
| 160. #101 | Dic9 | semidirect |
| 161. #100 | Dic9 | semidirect |
| 236. C9 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#413 | 2 |
| #10588914 | 2 |
| C2×#63396 | 2 |
| M16×Dic9 | 2 |
| #10588800 | 2 |
| #10588235 | 2 |
| #10588232 | 2 |
| #70130 | 3 |