Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265892 | C2 | semidirect |
| 2. #20265832 | C2 | semidirect |
| 3. #20265528 | C2 | semidirect |
| 4. #20265519 | C2 | semidirect |
| 5. #20265468 | C2 | semidirect |
| 6. #20265406 | C2 | semidirect |
| 7. #20265383 | C2 | semidirect |
| 8. #20265324 | C2 | semidirect |
| 9. C4×D808 | C2 | semidirect |
| 10. #20265174 | C2 | semidirect |
| 11. C8×D4×C101 | C2 | semidirect |
| 131. C101 | #3303 | semidirect |
| 141. C8×D4 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265892 | 2 |
| #20265832 | 2 |
| #20265528 | 2 |
| #20265519 | 2 |
| #20265468 | 2 |
| #20265406 | 2 |
| #20265383 | 2 |
| #20265324 | 2 |
| C4×D808 | 2 |
| #20265174 | 2 |
| C8×D4×C101 | 2 |
| #3303 | 101 |