Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 3. #20261742 | C2 | semidirect |
| 4. #20261741 | C2 | semidirect |
| 5. #20261736 | C2 | semidirect |
| 15. #15690877 | C22 | semidirect |
| 16. C4⋊#11715897 | C22 | semidirect |
| 95. D97 | #424 | semidirect |
| 97. C97 | C2×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C22×#13095519 | 2 |
| #20261742 | 2 |
| #20261741 | 2 |
| #20261736 | 2 |
| #117×D97 | 2 |
| C2×#424 | 97 |