Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #20260776 | C2 | semidirect |
| 4. #20260774 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260771 | C2 | semidirect |
| 7. #427×C97 | C2 | semidirect |
| 9. C2×#13095494 | C4 | semidirect |
| 20. #15690744 | C22 | semidirect |
| 21. #15690743 | C22 | semidirect |
| 22. #15690742 | C22 | semidirect |
| 23. #15690741 | C22 | semidirect |
| 26. #107×C97 | C22 | semidirect |
| 27. #106×C97 | C22 | semidirect |
| 35. #13095494 | C2×C4 | semidirect |
| 36. #13095494 | C2×C4 | semidirect |
| 37. C2×#11715895 | C2×C4 | semidirect |
| 46. C2×C8×C97 | C2×C4 | semidirect |
| 88. C97 | #2911 | semidirect |
| 95. #427 | D97 | semidirect |
| 112. #107 | C2×D97 | semidirect |
| 115. #106 | C2×D97 | semidirect |
| 128. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| #117×D97 | 2 |
| #20260776 | 2 |
| #20260774 | 2 |
| #20260773 | 2 |
| #20260771 | 2 |
| #427×C97 | 2 |
| #2911 | 97 |