Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20265830 | C2 | semidirect |
| 3. #20265527 | C2 | semidirect |
| 4. #20265516 | C2 | semidirect |
| 5. #20265468 | C2 | semidirect |
| 6. #20265403 | C2 | semidirect |
| 7. #20265321 | C2 | semidirect |
| 8. C4×#13108059 | C2 | semidirect |
| 9. #20265242 | C2 | semidirect |
| 10. #20265172 | C2 | semidirect |
| 11. #461×C101 | C2 | semidirect |
| 131. C101 | #3303 | semidirect |
| 138. #461 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265892 | 2 |
| #20265830 | 2 |
| #20265527 | 2 |
| #20265516 | 2 |
| #20265468 | 2 |
| #20265403 | 2 |
| #20265321 | 2 |
| C4×#13108059 | 2 |
| #20265242 | 2 |
| #20265172 | 2 |
| #461×C101 | 2 |
| #3303 | 101 |