Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
168 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20266228 | C2 | semidirect |
| 3. #20266039 | C2 | semidirect |
| 4. Q8⋊#11717581 | C2 | semidirect |
| 6. #11717581⋊C8 | C2 | semidirect |
| 58. #11717581 | SD16 | semidirect |
| 78. C101 | #1582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266228 | 2 |
| D4×#11717581 | 2 |
| #20266039 | 2 |
| Q8⋊#11717581 | 2 |
| D4⋊#11717581 | 2 |
| #11717581⋊C8 | 2 |
| SD16×Dic101 | 2 |
| #1582 | 101 |