Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
146 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 56. #11717579 | Q16 | semidirect |
| 71. C101 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265573 | 2 |
| #20265469 | 2 |
| #20265388 | 2 |
| #20265304 | 2 |
| #20264929 | 2 |
| #20264922 | 2 |
| #333×C101 | 2 |
| #1692 | 101 |