Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #20264949 | C2 | semidirect |
| 5. #20264948 | C2 | semidirect |
| 6. #20264947 | C2 | semidirect |
| 7. #344×C101 | C2 | semidirect |
| 90. C101 | #1829 | semidirect |
| 97. #344 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265651 | 2 |
| C2×#15692171 | 2 |
| #20264949 | 2 |
| #20264948 | 2 |
| #20264947 | 2 |
| #344×C101 | 2 |
| #1829 | 101 |