Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20253833 | C2 | semidirect |
| 2. #20253388 | C2 | semidirect |
| 3. #20244187 | C2 | semidirect |
| 4. #20241788 | C2 | semidirect |
| 5. #20241787 | C2 | semidirect |
| 6. #20241218 | C2 | semidirect |
| 7. C47×#3100 | C2 | semidirect |
| 141. C2×C47⋊C8 | D8 | semidirect |
| 217. #3100 | D47 | semidirect |
| 254. C47 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253833 | 2 |
| #20253388 | 2 |
| #20244187 | 2 |
| #20241788 | 2 |
| #20241787 | 2 |
| #20241218 | 2 |
| C47×#3100 | 2 |
| #10032 | 47 |