Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265573 | C2 | semidirect |
| 3. #20265498 | C2 | semidirect |
| 4. #20265495 | C2 | semidirect |
| 5. #20265467 | C2 | semidirect |
| 6. #20265454 | C2 | semidirect |
| 7. #20265428 | C2 | semidirect |
| 8. C4×#13108059 | C2 | semidirect |
| 9. #20265255 | C2 | semidirect |
| 10. #20265217 | C2 | semidirect |
| 11. #547×C101 | C2 | semidirect |
| 101. #11717579 | #41 | semidirect |
| 128. C101 | #3354 | semidirect |
| 130. #547 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265892 | 2 |
| #20265573 | 2 |
| #20265498 | 2 |
| #20265495 | 2 |
| #20265467 | 2 |
| #20265454 | 2 |
| #20265428 | 2 |
| C4×#13108059 | 2 |
| #20265255 | 2 |
| #20265217 | 2 |
| #547×C101 | 2 |
| #3354 | 101 |