Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
618 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 146 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. C22×#3667 | C2 | semidirect |
| 3. C9×#380 | C2 | semidirect |
| 4. C2×#63369 | C2 | semidirect |
| 5. #10588206 | C2 | semidirect |
| 13. #63492 | C4 | semidirect |
| 51. C2×C9⋊C8 | D4 | semidirect |
| 100. #380 | D9 | semidirect |
| 247. C9 | #1895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63492 | 2 |
| C22×#3667 | 2 |
| C9×#380 | 2 |
| C2×#63369 | 2 |
| #10588206 | 2 |
| #69517 | 3 |