Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 158 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. #10588132 | C2 | semidirect |
| 4. #10588131 | C2 | semidirect |
| 5. C8×C9⋊C8 | C2 | semidirect |
| 50. C8×C9 | M16 | semidirect |
| 52. C9⋊C8 | M16 | semidirect |
| 117. C9 | #1455 | semidirect |
| 128. C8 | #3667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×M16 | 2 |
| C4×#3667 | 2 |
| #10588132 | 2 |
| #10588131 | 2 |
| C8×C9⋊C8 | 2 |
| #69849 | 3 |