Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. C2×#15688938 | C2 | semidirect |
| 4. C2×#15688928 | C2 | semidirect |
| 6. #20241498 | C2 | semidirect |
| 7. C47×#1381 | C2 | semidirect |
| 17. #15689399 | C4 | semidirect |
| 171. #1381 | D47 | semidirect |
| 198. C47 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689539 | 2 |
| C2×#15689399 | 2 |
| C2×#15688938 | 2 |
| C2×#15688928 | 2 |
| #20243449 | 2 |
| #20241498 | 2 |
| C47×#1381 | 2 |
| #13072 | 47 |