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 |
|---|---|---|
| 3. #20261742 | C2 | semidirect |
| 4. #20261741 | C2 | semidirect |
| 5. #20261740 | C2 | semidirect |
| 6. #20261739 | C2 | semidirect |
| 17. #15690877 | C22 | semidirect |
| 18. C4⋊#11715897 | C22 | semidirect |
| 102. C97 | #2905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| C2×D97⋊M16 | 2 |
| #20261742 | 2 |
| #20261741 | 2 |
| #20261740 | 2 |
| #20261739 | 2 |
| #117×D97 | 2 |
| #2905 | 97 |