Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692254 | C2 | semidirect |
| 3. #20265471 | C2 | semidirect |
| 4. #20265466 | C2 | semidirect |
| 5. #20265461 | C2 | semidirect |
| 6. #20265456 | C2 | semidirect |
| 7. #20265220 | C2 | semidirect |
| 8. #20265200 | C2 | semidirect |
| 11. #428×C101 | C2 | semidirect |
| 44. #13108074 | Q8 | semidirect |
| 104. D404 | C2×Q8 | semidirect |
| 111. Dic202 | C2×Q8 | semidirect |
| 139. C101 | #3079 | semidirect |
| 147. #428 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692254 | 2 |
| #20265645 | 2 |
| #20265471 | 2 |
| #20265466 | 2 |
| #20265461 | 2 |
| #20265456 | 2 |
| #20265220 | 2 |
| #20265200 | 2 |
| #20265179 | 2 |
| #20265176 | 2 |
| #428×C101 | 2 |
| #3079 | 101 |