Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #20265905 | C2 | semidirect |
| 3. #20265528 | C2 | semidirect |
| 4. #20265526 | C2 | semidirect |
| 5. #20265462 | C2 | semidirect |
| 6. #20265461 | C2 | semidirect |
| 9. C8×Dic202 | C2 | semidirect |
| 95. Dic202 | SD16 | semidirect |
| 119. C101 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265905 | 2 |
| D4×Dic202 | 2 |
| #20265528 | 2 |
| #20265526 | 2 |
| #20265462 | 2 |
| #20265461 | 2 |
| #20265382 | 2 |
| #20265380 | 2 |
| C8×Dic202 | 2 |
| #20265268 | 2 |
| C4×SD16×C101 | 2 |
| #3359 | 101 |