Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20265517 | C2 | semidirect |
| 4. #20265473 | C2 | semidirect |
| 5. #20265467 | C2 | semidirect |
| 6. #20265384 | C2 | semidirect |
| 8. #20265281 | C2 | semidirect |
| 9. #20265278 | C2 | semidirect |
| 10. #20265233 | C2 | semidirect |
| 11. #461×C101 | C2 | semidirect |
| 137. C101 | #3116 | semidirect |
| 144. #461 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265732 | 2 |
| C4×#13108073 | 2 |
| #20265517 | 2 |
| #20265473 | 2 |
| #20265467 | 2 |
| #20265384 | 2 |
| #20265336 | 2 |
| #20265281 | 2 |
| #20265278 | 2 |
| #20265233 | 2 |
| #461×C101 | 2 |
| #3116 | 101 |