Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 3. #10588676 | C2 | semidirect |
| 4. C9×H(3,ℤ/4) | C2 | semidirect |
| 5. #10588237 | C2 | semidirect |
| 14. C2×#3663 | C4 | semidirect |
| 15. C2×C8×D9 | C4 | semidirect |
| 81. H(3,ℤ/4) | D9 | semidirect |
| 182. C9 | #1812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63469 | 2 |
| #10588686 | 2 |
| #10588676 | 2 |
| C9×H(3,ℤ/4) | 2 |
| #10588237 | 2 |
| #68710 | 3 |