Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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. #20261742 | C2 | semidirect |
| 3. #20261738 | C2 | semidirect |
| 9. #15690877 | C22 | semidirect |
| 10. C4⋊#11715897 | C22 | semidirect |
| 75. C97 | #2905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| #20261742 | 2 |
| #20261738 | 2 |
| C2×#15690768 | 2 |
| #2905 | 97 |