Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20265734 | C2 | semidirect |
| 2. #20265573 | C2 | semidirect |
| 3. #20265549 | C2 | semidirect |
| 4. #20265529 | C2 | semidirect |
| 5. #20265523 | C2 | semidirect |
| 6. #20265404 | C2 | semidirect |
| 7. C4×#13108062 | C2 | semidirect |
| 8. C2×C4×#11717579 | C2 | semidirect |
| 78. C2×C4×C101 | SD16 | semidirect |
| 90. #11717579 | #41 | semidirect |
| 113. C101 | #3167 | semidirect |
| 195. C2×C4 | #13108062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| #20265573 | 2 |
| #20265549 | 2 |
| #20265529 | 2 |
| #20265523 | 2 |
| #20265404 | 2 |
| C4×#13108062 | 2 |
| C2×C4×#11717579 | 2 |
| #532×C101 | 2 |
| #3167 | 101 |