Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C2×Q16×D101 | C2 | semidirect |
| 4. #20265556 | C2 | semidirect |
| 5. #20265417 | C2 | semidirect |
| 6. #20265388 | C2 | semidirect |
| 7. #20265334 | C2 | semidirect |
| 8. #20265331 | C2 | semidirect |
| 9. C4×#13108064 | C2 | semidirect |
| 11. #462×C101 | C2 | semidirect |
| 57. #13108064 | D4 | semidirect |
| 97. D404 | Q16 | semidirect |
| 114. C2×D101 | C2×Q16 | semidirect |
| 119. C4×C101 | C2×Q16 | semidirect |
| 131. C101 | D4×Q16 | semidirect |
| 138. #462 | D101 | semidirect |
| 254. C4 | Q16×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D101 | 2 |
| Q8×D404 | 2 |
| #20265842 | 2 |
| #20265556 | 2 |
| #20265417 | 2 |
| #20265388 | 2 |
| #20265334 | 2 |
| #20265331 | 2 |
| C4×#13108064 | 2 |
| #20265242 | 2 |
| #462×C101 | 2 |
| D4×Q16 | 101 |