Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20241921 | C2 | semidirect |
| 4. #20241752 | C2 | semidirect |
| 5. #20241297 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 27. C47×#484 | C4 | semidirect |
| 28. C47×#481 | C4 | semidirect |
| 32. C47×#451 | C4 | semidirect |
| 33. C47×#448 | C4 | semidirect |
| 227. #484 | Dic47 | semidirect |
| 228. #481 | Dic47 | semidirect |
| 232. #451 | Dic47 | semidirect |
| 233. #448 | Dic47 | semidirect |
| 251. C47 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252450 | 2 |
| #20241944 | 2 |
| #20241921 | 2 |
| #20241752 | 2 |
| #20241297 | 2 |
| #20241264 | 2 |
| C47×#3196 | 2 |
| #9331 | 47 |