Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
354 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 103 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×#15688947 | C2 | semidirect |
| 5. #20241488 | C2 | semidirect |
| 6. #20241472 | C2 | semidirect |
| 7. C47×#1778 | C2 | semidirect |
| 16. #15688935 | C4 | semidirect |
| 136. #1778 | D47 | semidirect |
| 158. C47 | #13138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688947 | 2 |
| C2×#15688935 | 2 |
| #20244264 | 2 |
| #20241488 | 2 |
| #20241472 | 2 |
| C47×#1778 | 2 |
| #13138 | 47 |