Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#15690843 | C2 | semidirect |
| 2. C2×#15690840 | C2 | semidirect |
| 4. C2×#15690775 | C2 | semidirect |
| 5. #20260960 | C2 | semidirect |
| 6. #20260956 | C2 | semidirect |
| 7. #20260944 | C2 | semidirect |
| 8. #20260934 | C2 | semidirect |
| 9. #20260758 | C2 | semidirect |
| 10. #20260734 | C2 | semidirect |
| 11. #417×C97 | C2 | semidirect |
| 49. C2×Dic194 | D4 | semidirect |
| 150. Dic97 | #137 | semidirect |
| 158. C97 | #3037 | semidirect |
| 169. #417 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| C2×#15690840 | 2 |
| #20261281 | 2 |
| C2×#15690775 | 2 |
| #20260960 | 2 |
| #20260956 | 2 |
| #20260944 | 2 |
| #20260934 | 2 |
| #20260758 | 2 |
| #20260734 | 2 |
| #417×C97 | 2 |
| #3037 | 97 |