Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20260631 | C2 | semidirect |
| 4. #20260626 | C2 | semidirect |
| 5. #20260597 | C2 | semidirect |
| 6. #20260594 | C2 | semidirect |
| 7. #20260581 | C2 | semidirect |
| 8. C4×C4⋊C4×C97 | C2 | semidirect |
| 11. C4×D388 | C4 | semidirect |
| 97. C97 | #2319 | semidirect |
| 104. 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 |
| #20260636 | 2 |
| #20260631 | 2 |
| #20260626 | 2 |
| #20260597 | 2 |
| #20260594 | 2 |
| #20260581 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #2319 | 97 |