Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. Q8×D404 | C2 | semidirect |
| 3. #20265529 | C2 | semidirect |
| 4. #20265509 | C2 | semidirect |
| 5. #20265407 | C2 | semidirect |
| 6. #20265383 | C2 | semidirect |
| 7. #20265317 | C2 | semidirect |
| 8. C4×#13108061 | C2 | semidirect |
| 9. #20265242 | C2 | semidirect |
| 10. #103×D101 | C2 | semidirect |
| 11. #475×C101 | C2 | semidirect |
| 81. Q8×C101 | #41 | semidirect |
| 94. D404 | SD16 | semidirect |
| 129. C101 | #3298 | semidirect |
| 134. #475 | D101 | semidirect |
| 213. Q8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D404 | 2 |
| #20265830 | 2 |
| #20265529 | 2 |
| #20265509 | 2 |
| #20265407 | 2 |
| #20265383 | 2 |
| #20265317 | 2 |
| C4×#13108061 | 2 |
| #20265242 | 2 |
| #103×D101 | 2 |
| #475×C101 | 2 |
| #3298 | 101 |