Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#15690885 | C2 | semidirect |
| 2. #20261791 | C2 | semidirect |
| 3. #20261634 | C2 | semidirect |
| 4. #20261633 | C2 | semidirect |
| 9. #15690884 | C22 | semidirect |
| 11. C2×#13095514 | C22 | semidirect |
| 103. C97 | #2117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690885 | 2 |
| #20261791 | 2 |
| #20261634 | 2 |
| #20261633 | 2 |
| #131×D97 | 2 |
| #2117 | 97 |