Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20252239 | C2 | semidirect |
| 3. #20245263 | C2 | semidirect |
| 4. #20245234 | C2 | semidirect |
| 5. #20245103 | C2 | semidirect |
| 6. #20244984 | C2 | semidirect |
| 7. C47×#2158 | C2 | semidirect |
| 10. C2×D752 | C4 | semidirect |
| 15. #15689205 | C22 | semidirect |
| 18. #15688923 | C22 | semidirect |
| 19. #15688898 | C22 | semidirect |
| 20. C16×Dic47 | C22 | semidirect |
| 23. C47×#367 | C22 | semidirect |
| 24. C47×#366 | C22 | semidirect |
| 28. C2×D376 | C2×C4 | semidirect |
| 35. D752 | C2×C4 | semidirect |
| 36. D752 | C2×C4 | semidirect |
| 44. C2×C16×C47 | C2×C4 | semidirect |
| 109. #2158 | D47 | semidirect |
| 128. #367 | C2×D47 | semidirect |
| 129. #366 | C2×D47 | semidirect |
| 133. C47 | #33456 | semidirect |
| 150. C2×C16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D752 | 2 |
| #20252239 | 2 |
| #20245263 | 2 |
| #20245234 | 2 |
| #20245103 | 2 |
| #20244984 | 2 |
| C47×#2158 | 2 |
| #33456 | 47 |