Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20265708 | C2 | semidirect |
| 2. #20265578 | C2 | semidirect |
| 3. #20265560 | C2 | semidirect |
| 4. #20265530 | C2 | semidirect |
| 5. #20265418 | C2 | semidirect |
| 6. #20265404 | C2 | semidirect |
| 7. #20265271 | C2 | semidirect |
| 8. #20265268 | C2 | semidirect |
| 9. D8×Dic101 | C2 | semidirect |
| 10. C2×C8×Dic101 | C2 | semidirect |
| 119. C101 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265708 | 2 |
| #20265578 | 2 |
| #20265560 | 2 |
| #20265530 | 2 |
| #20265418 | 2 |
| #20265404 | 2 |
| #20265271 | 2 |
| #20265268 | 2 |
| D8×Dic101 | 2 |
| C2×C8×Dic101 | 2 |
| #466×C101 | 2 |
| #3168 | 101 |