Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. #20266039 | C2 | semidirect |
| 4. #20266038 | C2 | semidirect |
| 66. C101 | #1570 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266181 | 2 |
| D101⋊(C4⋊C8) | 2 |
| #20266039 | 2 |
| #20266038 | 2 |
| #20265229 | 2 |
| #1570 | 101 |