Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 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. #20261750 | C2 | semidirect |
| 3. D97⋊#108 | C2 | semidirect |
| 12. #15690881 | C22 | semidirect |
| 13. #15690880 | C22 | semidirect |
| 94. D97 | #430 | semidirect |
| 96. C97 | C2×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| #20261750 | 2 |
| D97⋊#108 | 2 |
| C2×M16×D97 | 2 |
| C2×#430 | 97 |