Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10588803 | C2 | semidirect |
| 3. #10588686 | C2 | semidirect |
| 4. #10588683 | C2 | semidirect |
| 5. C9×H(3,ℤ/4) | C2 | semidirect |
| 82. H(3,ℤ/4) | D9 | semidirect |
| 184. C9 | #2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589850 | 2 |
| #10588803 | 2 |
| #10588686 | 2 |
| #10588683 | 2 |
| C9×H(3,ℤ/4) | 2 |
| #68698 | 3 |