Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 198 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. C2×#15690881 | C2 | semidirect |
| 4. D97⋊#108 | C2 | semidirect |
| 74. C97 | #2916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261814 | 2 |
| #20261750 | 2 |
| C2×#15690881 | 2 |
| D97⋊#108 | 2 |
| #131×D97 | 2 |
| #2916 | 97 |