Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 3. #20260525 | C2 | semidirect |
| 12. C22×Q8×C97 | C4 | semidirect |
| 15. #123×C97 | C4 | semidirect |
| 19. #117×C97 | C4 | semidirect |
| 93. C97 | #2123 | semidirect |
| 99. C22×Q8 | Dic97 | semidirect |
| 103. #123 | Dic97 | semidirect |
| 108. #117 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260719 | 2 |
| #20260709 | 2 |
| #20260525 | 2 |
| #536×C97 | 2 |
| #2123 | 97 |