Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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×#15688960 | C2 | semidirect |
| 2. C2×#15688958 | C2 | semidirect |
| 3. #20245638 | C2 | semidirect |
| 4. #20241522 | C2 | semidirect |
| 5. C47×#2249 | C2 | semidirect |
| 23. C47⋊C32 | D4 | semidirect |
| 79. #2249 | D47 | semidirect |
| 97. C47 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688960 | 2 |
| C2×#15688958 | 2 |
| #20245638 | 2 |
| #20241522 | 2 |
| C47×#2249 | 2 |
| #13729 | 47 |