Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D101 | C2 | semidirect |
| 3. #20265472 | C2 | semidirect |
| 4. #20265468 | C2 | semidirect |
| 5. #20265464 | C2 | semidirect |
| 6. #20265460 | C2 | semidirect |
| 7. #20265456 | C2 | semidirect |
| 8. #20265218 | C2 | semidirect |
| 9. #20265199 | C2 | semidirect |
| 11. #477×C101 | C2 | semidirect |
| 44. #13108075 | Q8 | semidirect |
| 86. Q8×C101 | C2×Q8 | semidirect |
| 100. D404 | C2×Q8 | semidirect |
| 138. C101 | #3079 | semidirect |
| 142. #477 | D101 | semidirect |
| 226. Q8 | Q8×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D101 | 2 |
| C4×#13108075 | 2 |
| #20265472 | 2 |
| #20265468 | 2 |
| #20265464 | 2 |
| #20265460 | 2 |
| #20265456 | 2 |
| #20265218 | 2 |
| #20265199 | 2 |
| #20265177 | 2 |
| #477×C101 | 2 |
| #3079 | 101 |