Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 474 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. C9×#407 | C2 | semidirect |
| 3. #10588887 | C2 | semidirect |
| 4. #10588146 | C2 | semidirect |
| 5. #10588145 | C2 | semidirect |
| 89. C22×D9 | M16 | semidirect |
| 108. C2×Dic9 | M16 | semidirect |
| 115. #407 | D9 | semidirect |
| 290. C9 | #1465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#611 | 2 |
| C9×#407 | 2 |
| #10588887 | 2 |
| #10588146 | 2 |
| #10588145 | 2 |
| #69968 | 3 |