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. #20265848 | C2 | semidirect |
| 2. D4×Dic202 | C2 | semidirect |
| 3. #20265524 | C2 | semidirect |
| 4. #20265522 | C2 | semidirect |
| 5. #20265457 | C2 | semidirect |
| 6. #20265456 | C2 | semidirect |
| 7. #20265372 | C2 | semidirect |
| 8. #20265370 | C2 | semidirect |
| 9. C8×Dic202 | C2 | semidirect |
| 10. #20265257 | C2 | semidirect |
| 11. C4×D8×C101 | C2 | semidirect |
| 81. D4×C101 | #41 | semidirect |
| 102. Dic202 | D8 | semidirect |
| 132. C101 | #3358 | semidirect |
| 143. C4×D8 | D101 | semidirect |
| 222. D4 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265848 | 2 |
| D4×Dic202 | 2 |
| #20265524 | 2 |
| #20265522 | 2 |
| #20265457 | 2 |
| #20265456 | 2 |
| #20265372 | 2 |
| #20265370 | 2 |
| C8×Dic202 | 2 |
| #20265257 | 2 |
| C4×D8×C101 | 2 |
| #3358 | 101 |