Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15692288 | C2 | semidirect |
| 2. C2×#15692263 | C2 | semidirect |
| 4. #20265753 | C2 | semidirect |
| 5. #20265436 | C2 | semidirect |
| 6. #20265424 | C2 | semidirect |
| 7. #20265419 | C2 | semidirect |
| 8. #20265407 | C2 | semidirect |
| 9. #20265171 | C2 | semidirect |
| 10. C2×#15692178 | C2 | semidirect |
| 11. #428×C101 | C2 | semidirect |
| 77. M16×C101 | D4 | semidirect |
| 144. C101 | #3063 | semidirect |
| 153. #428 | D101 | semidirect |
| 210. M16 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| C2×#15692263 | 2 |
| #20265758 | 2 |
| #20265753 | 2 |
| #20265436 | 2 |
| #20265424 | 2 |
| #20265419 | 2 |
| #20265407 | 2 |
| #20265171 | 2 |
| C2×#15692178 | 2 |
| #428×C101 | 2 |
| #3063 | 101 |