Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265906 | C2 | semidirect |
| 3. #20265533 | C2 | semidirect |
| 5. #20265480 | C2 | semidirect |
| 6. #20265462 | C2 | semidirect |
| 7. #20265401 | C2 | semidirect |
| 9. C8×Dic202 | C2 | semidirect |
| 10. #20265262 | C2 | semidirect |
| 11. C4×Q16×C101 | C2 | semidirect |
| 118. C101 | #3365 | semidirect |
| 128. C4×Q16 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265912 | 2 |
| #20265906 | 2 |
| #20265533 | 2 |
| #20265524 | 2 |
| #20265480 | 2 |
| #20265462 | 2 |
| #20265401 | 2 |
| #20265377 | 2 |
| C8×Dic202 | 2 |
| #20265262 | 2 |
| C4×Q16×C101 | 2 |
| #3365 | 101 |