Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20265536 | C2 | semidirect |
| 3. #20265531 | C2 | semidirect |
| 4. #20265186 | C2 | semidirect |
| 6. C4×#13108058 | C2 | semidirect |
| 9. #15692255 | C22 | semidirect |
| 10. #15692247 | C22 | semidirect |
| 14. #15692179 | C22 | semidirect |
| 16. #15692166 | C22 | semidirect |
| 17. C4×#11717579 | C22 | semidirect |
| 84. C101 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| #20265536 | 2 |
| #20265531 | 2 |
| #20265186 | 2 |
| #20265182 | 2 |
| C4×#13108058 | 2 |
| C2×#124×C101 | 2 |
| #3140 | 101 |