Finite Group DatabasebetaFinite Group DatabasebetaOrder 972.
167 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 44 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. C22×#737 | C3 | semidirect |
| 2. #66436 | C3 | semidirect |
| 3. C3×C9×A4 | C3 | semidirect |
| 4. #66366 | C3 | semidirect |
| 5. #66365 | C3 | semidirect |
| 6. #66364 | C3 | semidirect |
| 7. #66363 | C3 | semidirect |
| 8. #66362 | C3 | semidirect |
| 9. #66361 | C3 | semidirect |
| 28. #737 | A4 | semidirect |
| 93. C22 | #6908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#737 | 3 |
| #66436 | 3 |
| C3×C9×A4 | 3 |
| #66366 | 3 |
| #66365 | 3 |
| #66364 | 3 |
| #66363 | 3 |
| #66362 | 3 |
| #66361 | 3 |
| #6908 | 4 |