Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 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. #20266228 | C2 | semidirect |
| 2. #20266210 | C2 | semidirect |
| 3. #20266208 | C2 | semidirect |
| 4. #20266206 | C2 | semidirect |
| 5. #20266201 | C2 | semidirect |
| 6. #20266200 | C2 | semidirect |
| 7. #20266141 | C2 | semidirect |
| 8. C4×#13108084 | C2 | semidirect |
| 112. C101 | #2967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266228 | 2 |
| #20266210 | 2 |
| #20266208 | 2 |
| #20266206 | 2 |
| #20266201 | 2 |
| #20266200 | 2 |
| #20266141 | 2 |
| C4×#13108084 | 2 |
| #20265706 | 2 |
| #2967 | 101 |