Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20261210 | C2 | semidirect |
| 3. #20260741 | C2 | semidirect |
| 4. #20260496 | C2 | semidirect |
| 5. C2×#100×C97 | C2 | semidirect |
| 9. #15690806 | C4 | semidirect |
| 22. C2×D388 | C2×C4 | semidirect |
| 27. C4⋊Dic97 | D4 | semidirect |
| 32. C4×Dic97 | C2×C4 | semidirect |
| 88. C97 | #1887 | semidirect |
| 92. C2×#100 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| #20261210 | 2 |
| #20260741 | 2 |
| #20260496 | 2 |
| C2×#100×C97 | 2 |
| #1887 | 97 |