Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #20265543 | C2 | direct (N × H) |
| 3. C2×#15692175 | C2 | semidirect |
| 4. C2×#15692166 | C2 | semidirect |
| 5. C2×#125×C101 | C2 | semidirect |
| 11. #15692175 | C22 | semidirect |
| 12. #15692166 | C22 | semidirect |
| 14. #125×C101 | C22 | semidirect |
| 59. C2×C101 | #490 | semidirect |
| 64. C101 | C2×#490 | semidirect |
| 66. C2×#125 | D101 | semidirect |
| 76. #125 | C2×D101 | semidirect |
| 124. C2 | #20265543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692252 | 2 |
| #20265543 | 2 |
| C2×#15692175 | 2 |
| C2×#15692166 | 2 |
| C2×#125×C101 | 2 |
| C2×#490 | 101 |