Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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. C22×#13095501 | C2 | semidirect |
| 3. C2×#15690810 | C2 | semidirect |
| 4. #20261130 | C2 | direct (N × H) |
| 5. C2×#15690721 | C2 | semidirect |
| 9. C2×#13095501 | C22 | semidirect |
| 14. #15690810 | C22 | semidirect |
| 16. #15690721 | C22 | semidirect |
| 79. C2×C97 | #497 | semidirect |
| 83. C97 | C2×#497 | semidirect |
| 162. C2 | #20261130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| C22×#13095499 | 2 |
| C2×#15690810 | 2 |
| #20261130 | 2 |
| C2×#15690721 | 2 |
| C2×#124×C97 | 2 |
| C2×#497 | 97 |