Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #20265528 | C2 | semidirect |
| 4. #20265513 | C2 | semidirect |
| 5. #20265473 | C2 | semidirect |
| 6. #20265418 | C2 | semidirect |
| 7. #20265388 | C2 | semidirect |
| 8. #20265335 | C2 | semidirect |
| 9. C4×Dic404 | C2 | semidirect |
| 10. C2×#15692180 | C2 | semidirect |
| 77. D4×C101 | Q16 | semidirect |
| 123. C101 | #3299 | semidirect |
| 208. D4 | Dic404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265884 | 2 |
| D4×Dic202 | 2 |
| #20265528 | 2 |
| #20265513 | 2 |
| #20265473 | 2 |
| #20265418 | 2 |
| #20265388 | 2 |
| #20265335 | 2 |
| C4×Dic404 | 2 |
| C2×#15692180 | 2 |
| C8×D4×C101 | 2 |
| #3299 | 101 |