Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #20260797 | C2 | semidirect |
| 3. #20260794 | C2 | semidirect |
| 4. #20260758 | C2 | semidirect |
| 6. C4×#13095495 | C2 | semidirect |
| 7. C4×M16×C97 | C2 | semidirect |
| 16. #15690739 | C22 | semidirect |
| 18. #15690721 | C22 | semidirect |
| 19. C4×#11715895 | C22 | semidirect |
| 22. #97×C97 | C22 | semidirect |
| 23. C4×C8×C97 | C22 | semidirect |
| 80. C97 | #2921 | semidirect |
| 87. C4×M16 | D97 | semidirect |
| 101. #97 | C2×D97 | semidirect |
| 103. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690767 | 2 |
| #20260797 | 2 |
| #20260794 | 2 |
| #20260758 | 2 |
| #20260698 | 2 |
| C4×#13095495 | 2 |
| C4×M16×C97 | 2 |
| #2921 | 97 |