Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 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 |
|---|---|---|
| 2. C2×#15690775 | C2 | semidirect |
| 4. #20260641 | C2 | semidirect |
| 5. #20260623 | C2 | semidirect |
| 6. #20260600 | C2 | semidirect |
| 7. C22⋊C4×Dic97 | C2 | semidirect |
| 8. C42×Dic97 | C2 | semidirect |
| 12. #15690797 | C4 | semidirect |
| 32. C2×Dic194 | C2×C4 | semidirect |
| 43. C22⋊Dic97 | C2×C4 | semidirect |
| 47. C4×Dic97 | C2×C4 | semidirect |
| 105. Dic97 | #124 | semidirect |
| 113. C97 | C4×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690797 | 2 |
| C2×#15690775 | 2 |
| C2×D4×Dic97 | 2 |
| #20260641 | 2 |
| #20260623 | 2 |
| #20260600 | 2 |
| C22⋊C4×Dic97 | 2 |
| C42×Dic97 | 2 |
| #390×C97 | 2 |
| C4×#124 | 97 |