Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
402 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20243560 | C2 | semidirect |
| 3. #20242123 | C2 | semidirect |
| 4. #20242121 | C2 | semidirect |
| 5. #20241840 | C2 | semidirect |
| 6. C47⋊#1309 | C2 | semidirect |
| 7. C47×#1492 | C2 | semidirect |
| 174. #1492 | D47 | semidirect |
| 201. C47 | #10530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254766 | 2 |
| #20243560 | 2 |
| #20242123 | 2 |
| #20242121 | 2 |
| #20241840 | 2 |
| C47⋊#1309 | 2 |
| C47×#1492 | 2 |
| #10530 | 47 |