Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15690840 | C2 | semidirect |
| 2. C2×#15690797 | C2 | semidirect |
| 3. #20260913 | C2 | direct (N × H) |
| 4. C2×#15690737 | C2 | semidirect |
| 5. C2×#15690727 | C2 | semidirect |
| 7. C22×Dic194 | C22 | semidirect |
| 9. #15690840 | C22 | semidirect |
| 12. C2×#13095495 | C22 | semidirect |
| 14. #15690797 | C22 | semidirect |
| 16. C2×C4×Dic97 | C22 | semidirect |
| 17. #15690737 | C22 | semidirect |
| 18. #15690727 | C22 | semidirect |
| 30. C2×Dic194 | C23 | semidirect |
| 36. #13095495 | C23 | semidirect |
| 40. C4×Dic97 | C23 | semidirect |
| 117. C2×C97 | #455 | semidirect |
| 120. C97 | C2×#455 | semidirect |
| 237. C2 | #20260913 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690797 | 2 |
| #20260913 | 2 |
| C2×#15690737 | 2 |
| C2×#15690727 | 2 |
| C2×H(5,𝔽2)×C97 | 2 |
| C2×#455 | 97 |