Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
306 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10588799 | C2 | semidirect |
| 5. C9×H(3,ℤ/4) | C2 | semidirect |
| 6. #10588209 | C2 | semidirect |
| 7. #10588209 | C2 | semidirect |
| 92. H(3,ℤ/4) | D9 | semidirect |
| 210. C9 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63383 | 2 |
| #10588799 | 2 |
| #10588682 | 2 |
| C9×H(3,ℤ/4) | 2 |
| #10588209 | 2 |
| #68706 | 3 |