Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #20265913 | C2 | semidirect |
| 2. #20265847 | C2 | semidirect |
| 3. #20265565 | C2 | semidirect |
| 4. #20265390 | C2 | semidirect |
| 5. #20265374 | C2 | semidirect |
| 6. #20265370 | C2 | semidirect |
| 7. #20265369 | C2 | semidirect |
| 8. #20265307 | C2 | semidirect |
| 9. #20265289 | C2 | semidirect |
| 10. C4×#13108063 | C2 | semidirect |
| 11. #493×C101 | C2 | semidirect |
| 107. C8×C101 | #41 | semidirect |
| 135. C101 | #3399 | semidirect |
| 139. #493 | D101 | semidirect |
| 243. C8 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265913 | 2 |
| #20265847 | 2 |
| #20265565 | 2 |
| #20265390 | 2 |
| #20265374 | 2 |
| #20265370 | 2 |
| #20265369 | 2 |
| #20265307 | 2 |
| #20265289 | 2 |
| C4×#13108063 | 2 |
| #493×C101 | 2 |
| #3399 | 101 |