Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15690840 | C2 | semidirect |
| 2. C2×#15690808 | C2 | semidirect |
| 3. #20260918 | C2 | direct (N × H) |
| 4. C2×#15690737 | C2 | semidirect |
| 5. C2×#15690729 | C2 | semidirect |
| 9. #15690840 | C22 | semidirect |
| 14. #15690808 | C22 | semidirect |
| 17. #15690737 | C22 | semidirect |
| 18. #15690729 | C22 | semidirect |
| 110. C2×C97 | #456 | semidirect |
| 113. C97 | C2×#456 | semidirect |
| 223. C2 | #20260918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690808 | 2 |
| #20260918 | 2 |
| C2×#15690737 | 2 |
| C2×#15690729 | 2 |
| C2×2−1+4×C97 | 2 |
| C2×#456 | 97 |