Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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. #20265912 | C2 | semidirect |
| 2. #20265564 | C2 | semidirect |
| 3. #20265553 | C2 | semidirect |
| 4. #20265392 | C2 | semidirect |
| 5. #20265374 | C2 | semidirect |
| 6. #20265372 | C2 | semidirect |
| 7. #20265369 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265287 | C2 | semidirect |
| 10. C4×#13108062 | C2 | semidirect |
| 11. #550×C101 | C2 | semidirect |
| 108. #11717579 | #41 | semidirect |
| 135. C101 | #3399 | semidirect |
| 137. #550 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265912 | 2 |
| #20265564 | 2 |
| #20265553 | 2 |
| #20265392 | 2 |
| #20265374 | 2 |
| #20265372 | 2 |
| #20265369 | 2 |
| #20265308 | 2 |
| #20265287 | 2 |
| C4×#13108062 | 2 |
| #550×C101 | 2 |
| #3399 | 101 |