Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1296 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20246002 | C2 | semidirect |
| 3. #20243320 | C2 | semidirect |
| 4. #20241268 | C2 | semidirect |
| 5. C2×C47×#323 | C2 | semidirect |
| 12. #15689032 | C4 | semidirect |
| 25. C22×D188 | C2×C4 | semidirect |
| 34. C2×C4⋊Dic47 | D4 | semidirect |
| 45. C47⋊#95 | C2×C4 | semidirect |
| 135. C23×C47 | #102 | semidirect |
| 236. C2×#323 | D47 | semidirect |
| 263. C47 | #9017 | semidirect |
| 402. C23 | #13093946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689032 | 2 |
| #20246002 | 2 |
| #20243320 | 2 |
| #20241268 | 2 |
| C2×C47×#323 | 2 |
| #9017 | 47 |