Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×#15690769 | C2 | semidirect |
| 3. #20260637 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. #20260590 | C2 | semidirect |
| 6. C2×#117×C97 | C2 | semidirect |
| 10. C22×D388 | C4 | semidirect |
| 14. C2×C4⋊Dic97 | C22 | semidirect |
| 16. C2×#13095488 | C22 | semidirect |
| 17. C2×C4×Dic97 | C22 | semidirect |
| 20. C2×C4⋊C4×C97 | C22 | semidirect |
| 22. C2×C42×C97 | C22 | semidirect |
| 65. C2×C4×C97 | C22⋊C4 | semidirect |
| 100. C97 | #2309 | semidirect |
| 103. C2×#117 | D97 | semidirect |
| 117. C2×C4⋊C4 | C2×D97 | semidirect |
| 122. C2×C42 | C2×D97 | semidirect |
| 169. C2×C4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C2×#15690769 | 2 |
| #20260637 | 2 |
| #20260636 | 2 |
| #20260590 | 2 |
| C2×#117×C97 | 2 |
| #2309 | 97 |