Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
604 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 221 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. #20260633 | C2 | semidirect |
| 4. #20260620 | C2 | semidirect |
| 7. C4×C4⋊Dic97 | C2 | semidirect |
| 11. C2×C4⋊Dic97 | C4 | semidirect |
| 90. C4×C97 | #117 | semidirect |
| 101. C97 | #2344 | semidirect |
| 194. C4 | #15690766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690766 | 2 |
| C22×C4⋊Dic97 | 2 |
| #20260633 | 2 |
| #20260620 | 2 |
| #20260596 | 2 |
| #20260595 | 2 |
| C4×C4⋊Dic97 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #2344 | 97 |