Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×Q8×Dic101 | C2 | semidirect |
| 3. #20265513 | C2 | semidirect |
| 5. #20265486 | C2 | semidirect |
| 6. #20265397 | C2 | semidirect |
| 7. #20265333 | C2 | semidirect |
| 8. #20265281 | C2 | semidirect |
| 9. #20265278 | C2 | semidirect |
| 10. #20265231 | C2 | semidirect |
| 132. C101 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265708 | 2 |
| C2×Q8×Dic101 | 2 |
| #20265513 | 2 |
| #20265493 | 2 |
| #20265486 | 2 |
| #20265397 | 2 |
| #20265333 | 2 |
| #20265281 | 2 |
| #20265278 | 2 |
| #20265231 | 2 |
| #448×C101 | 2 |
| #3117 | 101 |