Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20265529 | C2 | semidirect |
| 2. #20265528 | C2 | semidirect |
| 3. #20265527 | C2 | semidirect |
| 6. C8×#11717579 | C2 | semidirect |
| 68. C101 | #1711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265529 | 2 |
| #20265528 | 2 |
| #20265527 | 2 |
| #20265523 | 2 |
| C8×#11717579 | 2 |
| #486×C101 | 2 |
| #1711 | 101 |