Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20256490 | C2 | semidirect |
| 3. #20245116 | C2 | semidirect |
| 4. #20243435 | C2 | semidirect |
| 5. #20241488 | C2 | semidirect |
| 6. #20241487 | C2 | semidirect |
| 7. C47×#2143 | C2 | semidirect |
| 45. C2×C47⋊C16 | D4 | semidirect |
| 67. C2×C16×C47 | D4 | semidirect |
| 178. #2143 | D47 | semidirect |
| 207. C47 | #13076 | semidirect |
| 240. C2×C16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256490 | 2 |
| #20253046 | 2 |
| #20245116 | 2 |
| #20243435 | 2 |
| #20241488 | 2 |
| #20241487 | 2 |
| C47×#2143 | 2 |
| #13076 | 47 |