Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 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. #20265849 | C2 | semidirect |
| 2. #20265567 | C2 | semidirect |
| 3. #20265551 | C2 | semidirect |
| 4. #20265389 | C2 | semidirect |
| 5. #20265379 | C2 | semidirect |
| 6. #20265377 | C2 | semidirect |
| 7. #20265372 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265275 | C2 | semidirect |
| 10. C4×#13108059 | C2 | semidirect |
| 11. #556×C101 | C2 | semidirect |
| 106. #11717579 | #41 | semidirect |
| 133. C101 | #3397 | semidirect |
| 134. #556 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265849 | 2 |
| #20265567 | 2 |
| #20265551 | 2 |
| #20265389 | 2 |
| #20265379 | 2 |
| #20265377 | 2 |
| #20265372 | 2 |
| #20265308 | 2 |
| #20265275 | 2 |
| C4×#13108059 | 2 |
| #556×C101 | 2 |
| #3397 | 101 |