Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 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. #20261686 | C2 | semidirect |
| 3. #20261685 | C2 | semidirect |
| 4. #20261678 | C2 | semidirect |
| 5. #20261677 | C2 | semidirect |
| 6. C4×C4⋊#87604 | C2 | semidirect |
| 7. #20261671 | C2 | semidirect |
| 22. C4×D388 | C4 | semidirect |
| 23. D4×Dic97 | C4 | semidirect |
| 24. #15690772 | C4 | semidirect |
| 25. C4×C22⋊D97 | C4 | semidirect |
| 26. #15690770 | C4 | semidirect |
| 30. C4×D4×C97 | C4 | semidirect |
| 133. C97 | #2319 | semidirect |
| 149. C4×D4 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261687 | 2 |
| #20261686 | 2 |
| #20261685 | 2 |
| #20261678 | 2 |
| #20261677 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261671 | 2 |
| C4×D4×D97 | 2 |
| #2319 | 97 |