Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20261213 | C2 | semidirect |
| 4. #20260838 | C2 | semidirect |
| 5. #20260820 | C2 | semidirect |
| 6. #20260771 | C2 | semidirect |
| 8. #20260693 | C2 | semidirect |
| 9. #419×C97 | C2 | semidirect |
| 11. C2×#13095498 | C4 | semidirect |
| 16. Q8×Dic97 | C22 | semidirect |
| 23. #15690743 | C22 | semidirect |
| 24. #15690741 | C22 | semidirect |
| 26. #15690720 | C22 | semidirect |
| 27. C8×Dic97 | C22 | semidirect |
| 31. #103×C97 | C22 | semidirect |
| 38. #13095498 | C2×C4 | semidirect |
| 39. #13095498 | C2×C4 | semidirect |
| 40. C2×#11715895 | C2×C4 | semidirect |
| 54. C2×Q8×C97 | C2×C4 | semidirect |
| 104. C97 | #2949 | semidirect |
| 111. #419 | D97 | semidirect |
| 132. #103 | C2×D97 | semidirect |
| 139. C2×Q8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| #20261213 | 2 |
| #20261209 | 2 |
| #20260838 | 2 |
| #20260820 | 2 |
| #20260771 | 2 |
| #20260741 | 2 |
| #20260693 | 2 |
| #419×C97 | 2 |
| #2949 | 97 |