Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
471 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 471 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. #10589618 | C2 | semidirect |
| 4. C2×#63382 | C2 | semidirect |
| 6. C9×H(3,ℤ/4) | C2 | semidirect |
| 7. #10588210 | C2 | semidirect |
| 20. #63437 | C4 | semidirect |
| 21. #63431 | C4 | semidirect |
| 121. H(3,ℤ/4) | D9 | semidirect |
| 273. C9 | #1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589628 | 2 |
| #10589618 | 2 |
| #10588819 | 2 |
| C2×#63382 | 2 |
| #10588685 | 2 |
| C9×H(3,ℤ/4) | 2 |
| #10588210 | 2 |
| #68708 | 3 |