Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
524 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 205 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. #20260619 | C2 | semidirect |
| 4. C4×#13095490 | C2 | semidirect |
| 6. #20260581 | C2 | semidirect |
| 7. C43×C97 | C2 | semidirect |
| 9. #15690767 | C4 | semidirect |
| 76. C97 | #2298 | semidirect |
| 83. C43 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690767 | 2 |
| #20260626 | 2 |
| #20260619 | 2 |
| C4×#13095490 | 2 |
| C4×#13095488 | 2 |
| #20260581 | 2 |
| C43×C97 | 2 |
| #2298 | 97 |