Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20251352 | C2 | semidirect |
| 4. #20241214 | C2 | semidirect |
| 5. #20241213 | C2 | semidirect |
| 6. #20241210 | C2 | semidirect |
| 69. C2×Q8×C47 | SD16 | semidirect |
| 113. C4⋊Dic47 | SD16 | semidirect |
| 243. C47 | #7748 | semidirect |
| 290. C2×Q8 | #10625335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251352 | 2 |
| #20244619 | 2 |
| #20244476 | 2 |
| #20241214 | 2 |
| #20241213 | 2 |
| #20241210 | 2 |
| C47×#2014 | 2 |
| #7748 | 47 |