Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265900 | C2 | semidirect |
| 2. #20265534 | C2 | semidirect |
| 3. #20265529 | C2 | semidirect |
| 4. #20265481 | C2 | semidirect |
| 5. #20265464 | C2 | semidirect |
| 7. #20265382 | C2 | semidirect |
| 8. Q8×#11717579 | C2 | semidirect |
| 9. C4×#13108062 | C2 | semidirect |
| 11. #554×C101 | C2 | semidirect |
| 121. C101 | #3360 | semidirect |
| 123. #554 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| #20265534 | 2 |
| #20265529 | 2 |
| #20265481 | 2 |
| #20265464 | 2 |
| #20265392 | 2 |
| #20265382 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108062 | 2 |
| C4×#13108059 | 2 |
| #554×C101 | 2 |
| #3360 | 101 |