Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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. #20265732 | C2 | semidirect |
| 3. #20265544 | C2 | semidirect |
| 4. #20265540 | C2 | semidirect |
| 5. #20265539 | C2 | semidirect |
| 6. #20265537 | C2 | semidirect |
| 7. #20265536 | C2 | semidirect |
| 8. #20265172 | C2 | semidirect |
| 9. #20265170 | C2 | semidirect |
| 10. #97×D101 | C2 | semidirect |
| 11. #489×C101 | C2 | semidirect |
| 138. C101 | #3135 | semidirect |
| 146. #489 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265732 | 2 |
| #20265726 | 2 |
| #20265544 | 2 |
| #20265540 | 2 |
| #20265539 | 2 |
| #20265537 | 2 |
| #20265536 | 2 |
| #20265172 | 2 |
| #20265170 | 2 |
| #97×D101 | 2 |
| #489×C101 | 2 |
| #3135 | 101 |