Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20265304 | C2 | semidirect |
| 4. #20264907 | C2 | semidirect |
| 6. #20264899 | C2 | semidirect |
| 7. #334×C101 | C2 | semidirect |
| 60. #11717579 | SD16 | semidirect |
| 78. C101 | #1582 | semidirect |
| 82. #334 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265304 | 2 |
| C4×#13108063 | 2 |
| #20265242 | 2 |
| #20264907 | 2 |
| #20264904 | 2 |
| #20264899 | 2 |
| #334×C101 | 2 |
| #1582 | 101 |