Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15690802 | C2 | semidirect |
| 3. #20261036 | C2 | direct (N × H) |
| 4. C2×#15690744 | C2 | semidirect |
| 5. C2×#15690742 | C2 | semidirect |
| 8. C2×C4⋊C8×C97 | C2 | semidirect |
| 12. #15690802 | C22 | semidirect |
| 21. #15690744 | C22 | semidirect |
| 22. #15690742 | C22 | semidirect |
| 28. C4⋊C8×C97 | C22 | semidirect |
| 98. C2×C97 | #478 | semidirect |
| 104. C97 | C2×#478 | semidirect |
| 110. C2×C4⋊C8 | D97 | semidirect |
| 130. C4⋊C8 | C2×D97 | semidirect |
| 203. C2 | #20261036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690802 | 2 |
| C2×C4×D388 | 2 |
| #20261036 | 2 |
| C2×#15690744 | 2 |
| C2×#15690742 | 2 |
| C2×#15690732 | 2 |
| C2×C4⋊C8×C97 | 2 |
| C2×#478 | 97 |