Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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×#15690750 | C2 | semidirect |
| 3. #20260544 | C2 | semidirect |
| 4. #427×C97 | C2 | semidirect |
| 8. #15690832 | C4 | semidirect |
| 10. C2×Dic388 | C4 | semidirect |
| 12. C2×D776 | C4 | semidirect |
| 14. #15690750 | C22 | semidirect |
| 19. #106×C97 | C22 | semidirect |
| 85. C97 | #2145 | semidirect |
| 88. #427 | D97 | semidirect |
| 104. #106 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690750 | 2 |
| #20260544 | 2 |
| #427×C97 | 2 |
| #2145 | 97 |