Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #20265900 | C2 | semidirect |
| 3. #20265524 | C2 | semidirect |
| 4. #20265504 | C2 | semidirect |
| 5. #20265462 | C2 | semidirect |
| 6. #20265409 | C2 | semidirect |
| 7. #20265377 | C2 | semidirect |
| 8. #20265338 | C2 | semidirect |
| 9. C8×D404 | C2 | semidirect |
| 10. #20265172 | C2 | semidirect |
| 11. C4×Q16×C101 | C2 | semidirect |
| 128. C101 | #3304 | semidirect |
| 137. C4×Q16 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| #20265849 | 2 |
| #20265524 | 2 |
| #20265504 | 2 |
| #20265462 | 2 |
| #20265409 | 2 |
| #20265377 | 2 |
| #20265338 | 2 |
| C8×D404 | 2 |
| #20265172 | 2 |
| C4×Q16×C101 | 2 |
| #3304 | 101 |