Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20265994 | C2 | semidirect |
| 2. #20265618 | C2 | semidirect |
| 3. #20265617 | C2 | semidirect |
| 4. #20265607 | C2 | semidirect |
| 5. C2×#15692201 | C2 | semidirect |
| 6. #20265594 | C2 | semidirect |
| 7. #578×C101 | C2 | semidirect |
| 74. C101 | #3417 | semidirect |
| 76. #578 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265994 | 2 |
| #20265618 | 2 |
| #20265617 | 2 |
| #20265607 | 2 |
| C2×#15692201 | 2 |
| #20265594 | 2 |
| #578×C101 | 2 |
| #3417 | 101 |