Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
230 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 1. #20260762 | C2 | semidirect |
| 4. C2×C8×Dic97 | C2 | semidirect |
| 5. #20260500 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 19. #103×C97 | C4 | semidirect |
| 20. #102×C97 | C4 | semidirect |
| 91. C97 | #1937 | semidirect |
| 108. #103 | Dic97 | semidirect |
| 109. #102 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260762 | 2 |
| C2×#15690737 | 2 |
| #20260702 | 2 |
| C2×C8×Dic97 | 2 |
| #20260500 | 2 |
| #20260494 | 2 |
| #416×C97 | 2 |
| #1937 | 97 |