Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20260598 | C2 | semidirect |
| 3. #20260470 | C2 | semidirect |
| 4. #407×C97 | C2 | semidirect |
| 5. C22×D388 | C4 | semidirect |
| 9. #15690784 | C4 | semidirect |
| 11. C2×C4⋊Dic97 | C4 | semidirect |
| 15. #15690717 | C22 | semidirect |
| 19. C22⋊C8×C97 | C22 | semidirect |
| 103. C97 | #1510 | semidirect |
| 105. #407 | D97 | semidirect |
| 120. C22⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690784 | 2 |
| #20260598 | 2 |
| #20260470 | 2 |
| #407×C97 | 2 |
| #1510 | 97 |