Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 146 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. #20261600 | C2 | semidirect |
| 6. C2×#13095521 | C4 | semidirect |
| 9. C2×#13095520 | C4 | semidirect |
| 16. C2×#13095495 | C4 | semidirect |
| 17. C2×#13095494 | C4 | semidirect |
| 21. C2×M16×C97 | C4 | semidirect |
| 29. C2×#11715897 | C2×C4 | semidirect |
| 45. C2×#11715895 | C2×C4 | semidirect |
| 50. C2×C8×C97 | C2×C4 | semidirect |
| 60. C2×#87604 | M16 | semidirect |
| 106. C97 | #1728 | semidirect |
| 121. C2×M16 | #87604 | semidirect |
| 153. C2×C8 | C2×#87604 | 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×C4×#87604 | 2 |
| #20261600 | 2 |
| C2×M16×D97 | 2 |
| #1728 | 97 |