Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C22×C16×D47 | C2 | semidirect |
| 3. C2×#15688930 | C2 | semidirect |
| 4. #20243423 | C2 | semidirect |
| 5. #20241485 | C2 | semidirect |
| 6. #20241484 | C2 | semidirect |
| 7. C2×C47×#359 | C2 | semidirect |
| 44. C2×C47⋊C16 | D4 | semidirect |
| 65. C2×C16×C47 | D4 | semidirect |
| 167. C2×D47 | #359 | semidirect |
| 178. C2×#359 | D47 | semidirect |
| 207. C47 | #13063 | semidirect |
| 239. C2×C16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D47 | 2 |
| #20252965 | 2 |
| C2×#15688930 | 2 |
| #20243423 | 2 |
| #20241485 | 2 |
| #20241484 | 2 |
| C2×C47×#359 | 2 |
| #13063 | 47 |