Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 114 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. #20261624 | C2 | semidirect |
| 4. #20261621 | C2 | semidirect |
| 6. #15690884 | C4 | semidirect |
| 7. C2×#13095514 | C4 | semidirect |
| 50. C97 | #2108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690884 | 2 |
| C22×#13095514 | 2 |
| #20261624 | 2 |
| #20261621 | 2 |
| #20260693 | 2 |
| #2108 | 97 |