Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20260494 | C2 | semidirect |
| 14. #117×C97 | C4 | semidirect |
| 16. C2×C4⋊C4×C97 | C4 | semidirect |
| 17. C2×C4⋊C4×C97 | C4 | semidirect |
| 92. C97 | #1826 | semidirect |
| 101. #117 | Dic97 | semidirect |
| 103. C2×C4⋊C4 | Dic97 | semidirect |
| 104. C2×C4⋊C4 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260699 | 2 |
| C4×C22⋊Dic97 | 2 |
| #20260494 | 2 |
| C2×#117×C97 | 2 |
| #1826 | 97 |