Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #20265585 | C2 | semidirect |
| 4. #20265584 | C2 | semidirect |
| 5. #20265579 | C2 | semidirect |
| 6. #20265576 | C2 | semidirect |
| 7. #20265576 | C2 | semidirect |
| 11. #499×C101 | C2 | semidirect |
| 43. #13108057 | Q8 | semidirect |
| 44. #13108057 | Q8 | semidirect |
| 100. C101 | #3166 | semidirect |
| 108. #499 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265733 | 2 |
| #125×D101 | 2 |
| #20265585 | 2 |
| #20265584 | 2 |
| #20265579 | 2 |
| #20265576 | 2 |
| #20265218 | 2 |
| #20265216 | 2 |
| C4×#13108057 | 2 |
| #499×C101 | 2 |
| #3166 | 101 |