Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 64 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. #20261791 | C2 | semidirect |
| 2. D97⋊#108 | C2 | semidirect |
| 3. #20261653 | C2 | semidirect |
| 6. #15690885 | C22 | semidirect |
| 10. #15690880 | C22 | semidirect |
| 87. D97 | #361 | semidirect |
| 89. C97 | C2×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| D97⋊#108 | 2 |
| #20261653 | 2 |
| C2×D8×D97 | 2 |
| C2×#361 | 97 |