Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20254387 | C2 | semidirect |
| 3. #20242703 | C2 | semidirect |
| 4. #20242015 | C2 | semidirect |
| 5. #20241985 | C2 | semidirect |
| 6. C47×#3166 | C2 | semidirect |
| 14. #15689515 | C22 | semidirect |
| 15. #15689485 | C22 | semidirect |
| 20. #15688865 | C22 | semidirect |
| 21. #15688862 | C22 | semidirect |
| 24. C47×#501 | C22 | semidirect |
| 150. #3166 | D47 | semidirect |
| 167. #501 | C2×D47 | semidirect |
| 179. C47 | #19006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689871 | 2 |
| #20254387 | 2 |
| #20242703 | 2 |
| #20242015 | 2 |
| #20241985 | 2 |
| C47×#3166 | 2 |
| #19006 | 47 |