Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #20265556 | C2 | semidirect |
| 4. #20264929 | C2 | semidirect |
| 5. #20264923 | C2 | semidirect |
| 6. #20264922 | C2 | semidirect |
| 46. D4×C101 | Q16 | semidirect |
| 79. C101 | #1669 | semidirect |
| 127. D4 | #13108064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265556 | 2 |
| #20265457 | 2 |
| D4×#11717579 | 2 |
| #20264929 | 2 |
| #20264923 | 2 |
| #20264922 | 2 |
| #474×C101 | 2 |
| #1669 | 101 |