Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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×C16×Dic47 | C2 | semidirect |
| 4. #20244137 | C2 | semidirect |
| 5. #20241483 | C2 | semidirect |
| 6. #20241482 | C2 | semidirect |
| 21. C47×#358 | C4 | semidirect |
| 22. C47×#357 | C4 | semidirect |
| 156. #358 | Dic47 | semidirect |
| 157. #357 | Dic47 | semidirect |
| 160. C47 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688930 | 2 |
| C2×C16×Dic47 | 2 |
| #20244277 | 2 |
| #20244137 | 2 |
| #20241483 | 2 |
| #20241482 | 2 |
| C47×#2138 | 2 |
| #13151 | 47 |