Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#15689158 | C2 | semidirect |
| 3. C2×#15688934 | C2 | semidirect |
| 4. C2×#15688932 | C2 | semidirect |
| 5. #20244998 | C2 | semidirect |
| 6. #20241493 | C2 | semidirect |
| 7. C47×#1386 | C2 | semidirect |
| 13. #15689365 | C4 | semidirect |
| 14. #15689360 | C4 | semidirect |
| 58. #13093956 | D4 | semidirect |
| 70. #106×C47 | D4 | semidirect |
| 190. #1386 | D47 | semidirect |
| 216. C47 | #13002 | semidirect |
| 258. #106 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252970 | 2 |
| C2×#15689158 | 2 |
| C2×#15688934 | 2 |
| C2×#15688932 | 2 |
| #20244998 | 2 |
| #20241493 | 2 |
| C47×#1386 | 2 |
| #13002 | 47 |