Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20265873 | C2 | semidirect |
| 2. #20265579 | C2 | semidirect |
| 3. #20265502 | C2 | semidirect |
| 4. #20265491 | C2 | semidirect |
| 5. #20265478 | C2 | semidirect |
| 6. #20265430 | C2 | semidirect |
| 7. C4×D808 | C2 | semidirect |
| 8. #20265219 | C2 | semidirect |
| 9. #436×C101 | C2 | semidirect |
| 103. C101 | #3355 | semidirect |
| 111. #436 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265873 | 2 |
| #20265579 | 2 |
| #20265502 | 2 |
| #20265491 | 2 |
| #20265478 | 2 |
| #20265430 | 2 |
| C4×D808 | 2 |
| #20265219 | 2 |
| #436×C101 | 2 |
| #3355 | 101 |