Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265727 | C2 | semidirect |
| 2. #20265587 | C2 | semidirect |
| 3. #20265567 | C2 | semidirect |
| 4. #20265543 | C2 | semidirect |
| 5. #20265536 | C2 | semidirect |
| 6. #20265428 | C2 | semidirect |
| 7. #20265425 | C2 | semidirect |
| 8. C4×#13108061 | C2 | semidirect |
| 9. C4×#13108059 | C2 | semidirect |
| 10. C4×#13108058 | C2 | semidirect |
| 11. #529×C101 | C2 | semidirect |
| 110. #11717579 | #41 | semidirect |
| 138. C101 | #3171 | semidirect |
| 140. #529 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265727 | 2 |
| #20265587 | 2 |
| #20265567 | 2 |
| #20265543 | 2 |
| #20265536 | 2 |
| #20265428 | 2 |
| #20265425 | 2 |
| C4×#13108061 | 2 |
| C4×#13108059 | 2 |
| C4×#13108058 | 2 |
| #529×C101 | 2 |
| #3171 | 101 |