Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20264929 | C2 | semidirect |
| 5. #20264928 | C2 | semidirect |
| 6. #20264927 | C2 | semidirect |
| 7. #335×C101 | C2 | semidirect |
| 27. #13108057 | C8 | semidirect |
| 56. C8×C101 | C2×C8 | semidirect |
| 60. #11717579 | C2×C8 | semidirect |
| 78. C101 | #1565 | semidirect |
| 83. #335 | D101 | semidirect |
| 138. C8 | C8×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265229 | 2 |
| C4⋊C8×D101 | 2 |
| C4×#13108057 | 2 |
| #20264929 | 2 |
| #20264928 | 2 |
| #20264927 | 2 |
| #335×C101 | 2 |
| #1565 | 101 |