Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D101 | C2 | semidirect |
| 4. #20265436 | C2 | semidirect |
| 5. #20265435 | C2 | semidirect |
| 6. #20265432 | C2 | semidirect |
| 7. #20265417 | C2 | semidirect |
| 8. #20265416 | C2 | semidirect |
| 9. #20265212 | C2 | semidirect |
| 10. #20265184 | C2 | semidirect |
| 11. #470×C101 | C2 | semidirect |
| 134. C101 | #3059 | semidirect |
| 141. #470 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D101 | 2 |
| C2×#15692263 | 2 |
| #20265750 | 2 |
| #20265436 | 2 |
| #20265435 | 2 |
| #20265432 | 2 |
| #20265417 | 2 |
| #20265416 | 2 |
| #20265212 | 2 |
| #20265184 | 2 |
| #470×C101 | 2 |
| #3059 | 101 |