Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
207 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 122 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. C4⋊(C9⋊C16) | C2 | semidirect |
| 4. #10588138 | C2 | semidirect |
| 5. C4×C9⋊C16 | C2 | semidirect |
| 125. C9 | #2164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#405 | 2 |
| #10588226 | 2 |
| C4⋊(C9⋊C16) | 2 |
| #10588138 | 2 |
| C4×C9⋊C16 | 2 |
| #69883 | 3 |