Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
618 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 198 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 |
|---|---|---|
| 1. C2×C9×#125 | C2 | semidirect |
| 3. #10588749 | C2 | direct (N × H) |
| 5. C2×#63368 | C2 | semidirect |
| 6. C2×C4×C9⋊C8 | C2 | semidirect |
| 11. C9×#125 | C22 | semidirect |
| 20. #63368 | C22 | semidirect |
| 21. C4×C9⋊C8 | C22 | semidirect |
| 80. C2×#125 | D9 | semidirect |
| 120. #125 | C2×D9 | semidirect |
| 148. C2×C9 | #488 | semidirect |
| 182. C9 | C2×#488 | semidirect |
| 218. C2 | #10588749 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#125 | 2 |
| C2×#63437 | 2 |
| #10588749 | 2 |
| C2×#63369 | 2 |
| C2×#63368 | 2 |
| C2×C4×C9⋊C8 | 2 |
| C2×#5068 | 3 |