Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20251641 | C2 | direct (N × H) |
| 2. C2×#15689035 | C2 | semidirect |
| 5. C23×Dic94 | C22 | semidirect |
| 7. #15689035 | C22 | semidirect |
| 9. C2×C47⋊#95 | C22 | semidirect |
| 14. C22×Dic94 | C23 | semidirect |
| 18. C47⋊#95 | C23 | semidirect |
| 20. C25×C47 | Q8 | semidirect |
| 32. C24×C47 | C2×Q8 | semidirect |
| 77. C2×C47 | #2840 | semidirect |
| 88. C47 | C2×#2840 | semidirect |
| 90. C25 | Dic94 | semidirect |
| 108. C24 | C2×Dic94 | semidirect |
| 148. C2 | #20251641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251641 | 2 |
| C2×#15689035 | 2 |
| C2×#15688979 | 2 |
| C2×C47×#379 | 2 |
| C2×#2840 | 47 |