Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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. #20265912 | C2 | semidirect |
| 2. #20265849 | C2 | semidirect |
| 3. #20265566 | C2 | semidirect |
| 4. #20265554 | C2 | semidirect |
| 5. #20265393 | C2 | semidirect |
| 6. #20265378 | C2 | semidirect |
| 7. #20265373 | C2 | semidirect |
| 8. #20265373 | C2 | semidirect |
| 9. #20265290 | C2 | semidirect |
| 10. C4×#13108063 | C2 | semidirect |
| 11. #446×C101 | C2 | semidirect |
| 108. C8×C101 | #41 | semidirect |
| 135. C101 | #3399 | semidirect |
| 144. #446 | D101 | semidirect |
| 243. C8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265912 | 2 |
| #20265849 | 2 |
| #20265566 | 2 |
| #20265554 | 2 |
| #20265393 | 2 |
| #20265378 | 2 |
| #20265373 | 2 |
| #20265290 | 2 |
| C4×#13108063 | 2 |
| #446×C101 | 2 |
| #3399 | 101 |