Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
860 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 860 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20245059 | C2 | semidirect |
| 3. #20245053 | C2 | semidirect |
| 4. #20243915 | C2 | semidirect |
| 5. C47×#1884 | C2 | semidirect |
| 7. #15689865 | C4 | semidirect |
| 8. #15689839 | C4 | semidirect |
| 17. #15689097 | C22 | semidirect |
| 22. C47×#568 | C22 | semidirect |
| 25. C47×#410 | C22 | semidirect |
| 206. #1884 | D47 | semidirect |
| 213. #568 | C2×D47 | semidirect |
| 228. #410 | C2×D47 | semidirect |
| 234. C47 | #12778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257793 | 2 |
| #20245059 | 2 |
| #20245053 | 2 |
| #20243915 | 2 |
| C47×#1884 | 2 |
| #12778 | 47 |