Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1104 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 210 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. C2×#15690889 | C2 | semidirect |
| 2. #20261687 | C2 | semidirect |
| 3. #20261676 | C2 | semidirect |
| 6. C2×C4⋊#87604 | C22 | semidirect |
| 8. C2×C22⋊#87604 | C22 | semidirect |
| 9. C2×C4×#87604 | C22 | semidirect |
| 11. C22×D388 | C4 | semidirect |
| 12. C22×C22⋊D97 | C4 | semidirect |
| 14. C2×D4×D97 | C4 | semidirect |
| 17. C22×D4×C97 | C4 | semidirect |
| 63. C2×C4×C97 | C22⋊C4 | semidirect |
| 66. C2×Dic97 | C22⋊C4 | semidirect |
| 69. C4×D97 | C22⋊C4 | semidirect |
| 99. C97 | #2309 | semidirect |
| 110. C22×D4 | #87604 | semidirect |
| 169. C2×C4 | C22⋊#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261687 | 2 |
| #20261676 | 2 |
| C22×D4×D97 | 2 |
| #2309 | 97 |