Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20252023 | C2 | semidirect |
| 3. #20244236 | C2 | semidirect |
| 4. #20244226 | C2 | semidirect |
| 5. #20243316 | C2 | semidirect |
| 6. #20243308 | C2 | semidirect |
| 7. C47×#1785 | C2 | semidirect |
| 16. #15689146 | C22 | semidirect |
| 17. C2×#13093943 | C22 | semidirect |
| 18. C2×#13093941 | C22 | semidirect |
| 22. M16×Dic47 | C22 | semidirect |
| 24. C2×#101×C47 | C22 | semidirect |
| 25. C2×#100×C47 | C22 | semidirect |
| 180. #1785 | D47 | semidirect |
| 200. C2×#101 | C2×D47 | semidirect |
| 204. C2×#100 | C2×D47 | semidirect |
| 208. C47 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689687 | 2 |
| #20252023 | 2 |
| #20244236 | 2 |
| #20244226 | 2 |
| #20243316 | 2 |
| #20243308 | 2 |
| C47×#1785 | 2 |
| #21801 | 47 |