Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
4830 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 763 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. #20241659 | C2 | semidirect |
| 4. #20241658 | C2 | semidirect |
| 5. C47×#1446 | C2 | semidirect |
| 8. C22×Q8×D47 | C4 | semidirect |
| 19. C22×Dic94 | C2×C4 | semidirect |
| 29. C22×C4×D47 | Q8 | semidirect |
| 33. C22×Q8×C47 | C2×C4 | semidirect |
| 49. C22×C4×C47 | C2×Q8 | semidirect |
| 55. C22×Dic47 | C2×Q8 | semidirect |
| 111. #1446 | D47 | direct (N × H) |
| 116. D47 | #1446 | direct (N × H) |
| 127. C47 | C2×#1446 | semidirect |
| 135. C22×Q8 | C4×D47 | semidirect |
| 177. C22×C4 | Q8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×D47 | 2 |
| C2×#95×D47 | 2 |
| #20241659 | 2 |
| #20241658 | 2 |
| C47×#1446 | 2 |
| C2×#1446 | 47 |