Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
| 5. C2×#13095521 | C4 | semidirect |
| 8. C2×#13095520 | C4 | semidirect |
| 16. C22×#11715895 | C4 | semidirect |
| 19. C2×C8×D97 | C4 | semidirect |
| 21. C22×C8×C97 | C4 | semidirect |
| 103. C97 | #1729 | semidirect |
| 119. C22×C8 | #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 |
| C2×#15690889 | 2 |
| #20261600 | 2 |
| C22×C8×D97 | 2 |
| #1729 | 97 |