Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
604 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20245602 | C2 | direct (N × H) |
| 3. C2×#15688947 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. C2×#15688905 | C2 | semidirect |
| 6. C2×C47×#430 | C2 | semidirect |
| 14. #15688947 | C22 | semidirect |
| 15. #15688935 | C22 | semidirect |
| 16. #15688905 | C22 | semidirect |
| 20. C47×#430 | C22 | semidirect |
| 148. C2×#430 | D47 | semidirect |
| 156. C2×C47 | #2238 | semidirect |
| 167. #430 | C2×D47 | semidirect |
| 175. C47 | C2×#2238 | semidirect |
| 303. C2 | #20245602 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689376 | 2 |
| #20245602 | 2 |
| C2×#15688947 | 2 |
| C2×#15688935 | 2 |
| C2×#15688905 | 2 |
| C2×C47×#430 | 2 |
| C2×#2238 | 47 |