Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265847 | C2 | semidirect |
| 2. D4×Dic202 | C2 | semidirect |
| 3. #20265523 | C2 | semidirect |
| 4. #20265522 | C2 | semidirect |
| 5. #20265458 | C2 | semidirect |
| 6. #20265455 | C2 | semidirect |
| 7. #20265370 | C2 | semidirect |
| 8. #20265301 | C2 | semidirect |
| 9. D8×Dic101 | C2 | semidirect |
| 10. C4×#13108059 | C2 | semidirect |
| 11. #459×C101 | C2 | semidirect |
| 83. D4×C101 | #41 | semidirect |
| 102. Dic202 | D8 | semidirect |
| 132. C101 | #3358 | semidirect |
| 140. #459 | D101 | semidirect |
| 222. D4 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265847 | 2 |
| D4×Dic202 | 2 |
| #20265523 | 2 |
| #20265522 | 2 |
| #20265458 | 2 |
| #20265455 | 2 |
| #20265370 | 2 |
| #20265301 | 2 |
| D8×Dic101 | 2 |
| C4×#13108059 | 2 |
| #459×C101 | 2 |
| #3358 | 101 |