Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692255 | C2 | semidirect |
| 3. #20265473 | C2 | semidirect |
| 4. #20265468 | C2 | semidirect |
| 5. #20265463 | C2 | semidirect |
| 6. #20265458 | C2 | semidirect |
| 7. #20265219 | C2 | semidirect |
| 9. #423×C101 | C2 | semidirect |
| 36. #13108074 | Q8 | semidirect |
| 89. D404 | C2×Q8 | semidirect |
| 96. Dic202 | C2×Q8 | semidirect |
| 122. C101 | #3079 | semidirect |
| 130. #423 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692255 | 2 |
| C4×#13108074 | 2 |
| #20265473 | 2 |
| #20265468 | 2 |
| #20265463 | 2 |
| #20265458 | 2 |
| #20265219 | 2 |
| #20265179 | 2 |
| #423×C101 | 2 |
| #3079 | 101 |