Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
560 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 197 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. #20260625 | C2 | semidirect |
| 4. #20260601 | C2 | semidirect |
| 5. #20260597 | C2 | semidirect |
| 6. C4×C4⋊Dic97 | C2 | semidirect |
| 7. #20260582 | C2 | semidirect |
| 8. C4×C4⋊C4×C97 | C2 | semidirect |
| 11. C4×D388 | C4 | semidirect |
| 98. C97 | #2357 | semidirect |
| 105. C4×C4⋊C4 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| #20260637 | 2 |
| #20260625 | 2 |
| #20260601 | 2 |
| #20260597 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260582 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #2357 | 97 |