Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 162 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. #20261684 | C2 | semidirect |
| 3. #20261681 | C2 | semidirect |
| 4. #20261679 | C2 | semidirect |
| 6. C4×C4⋊#87604 | C2 | semidirect |
| 17. #15690769 | C4 | semidirect |
| 18. #15690768 | C4 | semidirect |
| 19. #15690767 | C4 | semidirect |
| 20. #15690767 | C4 | semidirect |
| 21. #15690766 | C4 | semidirect |
| 26. #117×C97 | C4 | semidirect |
| 122. C97 | #2314 | semidirect |
| 136. #117 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261685 | 2 |
| #20261684 | 2 |
| #20261681 | 2 |
| #20261679 | 2 |
| #20261677 | 2 |
| C4×C4⋊#87604 | 2 |
| #117×D97 | 2 |
| #2314 | 97 |