Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265892 | C2 | semidirect |
| 2. #20265831 | C2 | semidirect |
| 3. #20265575 | C2 | semidirect |
| 4. #20265502 | C2 | semidirect |
| 5. #20265496 | C2 | semidirect |
| 6. #20265468 | C2 | semidirect |
| 7. #20265458 | C2 | semidirect |
| 8. #20265430 | C2 | semidirect |
| 9. C4×D808 | C2 | semidirect |
| 10. #20265219 | C2 | semidirect |
| 11. #436×C101 | C2 | semidirect |
| 101. C8×C101 | #41 | semidirect |
| 128. C101 | #3354 | semidirect |
| 138. #436 | D101 | semidirect |
| 229. C8 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265892 | 2 |
| #20265831 | 2 |
| #20265575 | 2 |
| #20265502 | 2 |
| #20265496 | 2 |
| #20265468 | 2 |
| #20265458 | 2 |
| #20265430 | 2 |
| C4×D808 | 2 |
| #20265219 | 2 |
| #436×C101 | 2 |
| #3354 | 101 |