Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13095498 | C2 | semidirect |
| 3. #20261209 | C2 | semidirect |
| 4. #20260947 | C2 | semidirect |
| 5. #20260937 | C2 | semidirect |
| 6. #20260762 | C2 | semidirect |
| 7. #20260744 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 9. #536×C97 | C2 | semidirect |
| 22. C4⋊#11715895 | C22 | semidirect |
| 23. #15690734 | C22 | semidirect |
| 24. #15690734 | C22 | semidirect |
| 25. #15690731 | C22 | semidirect |
| 28. C4⋊Q8×C97 | C22 | semidirect |
| 29. #124×C97 | C22 | semidirect |
| 117. C97 | #3042 | semidirect |
| 120. #536 | D97 | semidirect |
| 137. C4⋊Q8 | C2×D97 | semidirect |
| 138. #124 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C22×#13095498 | 2 |
| #20261209 | 2 |
| #20260947 | 2 |
| #20260937 | 2 |
| #20260762 | 2 |
| #20260744 | 2 |
| #20260731 | 2 |
| #536×C97 | 2 |
| #3042 | 97 |