Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20265580 | C2 | semidirect |
| 3. #20265551 | C2 | semidirect |
| 4. #20265549 | C2 | semidirect |
| 5. #20265524 | C2 | semidirect |
| 6. C8×#11717579 | C2 | semidirect |
| 7. #486×C101 | C2 | semidirect |
| 56. #11717579 | D8 | semidirect |
| 57. #11717579 | SD16 | semidirect |
| 76. C101 | #1706 | semidirect |
| 82. #486 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265580 | 2 |
| #20265553 | 2 |
| #20265551 | 2 |
| #20265549 | 2 |
| #20265524 | 2 |
| C8×#11717579 | 2 |
| #486×C101 | 2 |
| #1706 | 101 |