Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. M32×D97 | C2 | semidirect |
| 3. #20260770 | C2 | semidirect |
| 4. #20260546 | C2 | semidirect |
| 5. #20260545 | C2 | semidirect |
| 6. #20260544 | C2 | semidirect |
| 7. #360×C97 | C2 | semidirect |
| 9. #15690833 | C4 | semidirect |
| 13. #15690829 | C4 | semidirect |
| 14. Q16×D97 | C4 | semidirect |
| 16. D8×D97 | C4 | semidirect |
| 19. #15690750 | C22 | semidirect |
| 23. #15690742 | C22 | semidirect |
| 25. M32×C97 | C22 | semidirect |
| 26. #106×C97 | C22 | semidirect |
| 111. C97 | #2145 | semidirect |
| 118. #360 | D97 | semidirect |
| 133. M32 | C2×D97 | semidirect |
| 137. #106 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D97 | 2 |
| M32×D97 | 2 |
| #20260770 | 2 |
| #20260546 | 2 |
| #20260545 | 2 |
| #20260544 | 2 |
| #360×C97 | 2 |
| #2145 | 97 |