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. Q8×Dic202 | C2 | semidirect |
| 3. #20265524 | C2 | semidirect |
| 4. #20265522 | C2 | semidirect |
| 5. #20265467 | C2 | semidirect |
| 6. #20265466 | C2 | semidirect |
| 7. #20265377 | C2 | semidirect |
| 8. #20265375 | C2 | semidirect |
| 9. C8×Dic202 | C2 | semidirect |
| 10. #20265262 | C2 | semidirect |
| 11. C4×SD16×C101 | C2 | semidirect |
| 77. Q8×C101 | #41 | semidirect |
| 99. Dic202 | SD16 | semidirect |
| 126. C101 | #3362 | semidirect |
| 137. C4×SD16 | D101 | semidirect |
| 206. Q8 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic202 | 2 |
| #20265848 | 2 |
| #20265524 | 2 |
| #20265522 | 2 |
| #20265467 | 2 |
| #20265466 | 2 |
| #20265377 | 2 |
| #20265375 | 2 |
| C8×Dic202 | 2 |
| #20265262 | 2 |
| C4×SD16×C101 | 2 |
| #3362 | 101 |