Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #20260699 | C2 | semidirect |
| 3. #20260458 | C2 | semidirect |
| 4. #407×C97 | C2 | semidirect |
| 15. C22⋊#11715895 | C22 | semidirect |
| 19. C22⋊C8×C97 | C22 | semidirect |
| 63. C22×D97 | M16 | semidirect |
| 111. C97 | #1462 | semidirect |
| 114. #407 | D97 | semidirect |
| 130. C22⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095488 | 2 |
| #20260699 | 2 |
| #20260458 | 2 |
| #407×C97 | 2 |
| #1462 | 97 |