Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20265711 | C2 | semidirect |
| 3. #20265586 | C2 | semidirect |
| 4. #20265566 | C2 | semidirect |
| 5. #20265542 | C2 | semidirect |
| 6. #20265537 | C2 | semidirect |
| 7. #20265430 | C2 | semidirect |
| 8. #20265423 | C2 | semidirect |
| 9. C4×#13108063 | C2 | semidirect |
| 10. C4×D808 | C2 | semidirect |
| 11. C4×M16×C101 | C2 | semidirect |
| 110. C8×C101 | #41 | semidirect |
| 138. C101 | #3171 | semidirect |
| 149. C4×M16 | D101 | semidirect |
| 248. C8 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265727 | 2 |
| #20265711 | 2 |
| #20265586 | 2 |
| #20265566 | 2 |
| #20265542 | 2 |
| #20265537 | 2 |
| #20265430 | 2 |
| #20265423 | 2 |
| C4×#13108063 | 2 |
| C4×D808 | 2 |
| C4×M16×C101 | 2 |
| #3171 | 101 |