Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #20265730 | C2 | semidirect |
| 3. #20265544 | C2 | semidirect |
| 4. #20265540 | C2 | semidirect |
| 5. #20265538 | C2 | semidirect |
| 6. #20265535 | C2 | semidirect |
| 7. #20265174 | C2 | semidirect |
| 8. #20265173 | C2 | semidirect |
| 9. #20265171 | C2 | semidirect |
| 10. C2×#15692165 | C2 | semidirect |
| 11. #416×C101 | C2 | semidirect |
| 126. C101 | #3135 | semidirect |
| 136. #416 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265730 | 2 |
| #20265723 | 2 |
| #20265544 | 2 |
| #20265540 | 2 |
| #20265538 | 2 |
| #20265535 | 2 |
| #20265174 | 2 |
| #20265173 | 2 |
| #20265171 | 2 |
| C2×#15692165 | 2 |
| #416×C101 | 2 |
| #3135 | 101 |