Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20261348 | C2 | direct (N × H) |
| 2. C2×#15690810 | C2 | semidirect |
| 4. C2×#15690801 | C2 | semidirect |
| 6. C2×#15690775 | C2 | semidirect |
| 8. C2×#125×C97 | C2 | semidirect |
| 11. #15690810 | C22 | semidirect |
| 13. #15690801 | C22 | semidirect |
| 15. #15690775 | C22 | semidirect |
| 25. #125×C97 | C22 | semidirect |
| 81. C2×C97 | #541 | semidirect |
| 86. C97 | C2×#541 | semidirect |
| 91. C2×#125 | D97 | semidirect |
| 100. #125 | C2×D97 | semidirect |
| 168. C2 | #20261348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261348 | 2 |
| C2×#15690810 | 2 |
| C2×#15690805 | 2 |
| C2×#15690801 | 2 |
| C2×#15690790 | 2 |
| C2×#15690775 | 2 |
| C2×#15690767 | 2 |
| C2×#125×C97 | 2 |
| C2×#541 | 97 |