Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20265553 | C2 | semidirect |
| 2. #20265553 | C2 | semidirect |
| 3. #20265549 | C2 | semidirect |
| 4. #20265524 | C2 | semidirect |
| 5. #20265523 | C2 | semidirect |
| 6. #20264899 | C2 | semidirect |
| 7. #493×C101 | C2 | semidirect |
| 60. #11717579 | D8 | semidirect |
| 82. C101 | #1721 | semidirect |
| 85. #493 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265553 | 2 |
| #20265549 | 2 |
| #20265524 | 2 |
| #20265523 | 2 |
| #20264899 | 2 |
| #493×C101 | 2 |
| #1721 | 101 |