Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #20265906 | C2 | semidirect |
| 3. #20265556 | C2 | semidirect |
| 5. #20265387 | C2 | semidirect |
| 6. #20265384 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265282 | C2 | semidirect |
| 120. C101 | #3398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265906 | 2 |
| #20265572 | 2 |
| #20265556 | 2 |
| #20265396 | 2 |
| #20265387 | 2 |
| #20265384 | 2 |
| #20265382 | 2 |
| #20265308 | 2 |
| #20265282 | 2 |
| C4×#13108062 | 2 |
| #556×C101 | 2 |
| #3398 | 101 |