Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20260773 | C2 | semidirect |
| 3. #20260492 | C2 | semidirect |
| 12. C2×M16×C97 | C4 | semidirect |
| 14. C22×C8×C97 | C4 | semidirect |
| 67. C97 | #1812 | semidirect |
| 75. C2×M16 | Dic97 | semidirect |
| 77. C22×C8 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260773 | 2 |
| #20260709 | 2 |
| #20260492 | 2 |
| C2×#131×C97 | 2 |
| #1812 | 97 |