Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
908 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 253 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. C22×#13095490 | C2 | semidirect |
| 4. #20260670 | C2 | direct (N × H) |
| 5. C2×#15690717 | C2 | semidirect |
| 6. C22×C4⋊C4×C97 | C2 | semidirect |
| 11. C2×#13095490 | C22 | semidirect |
| 16. #15690717 | C22 | semidirect |
| 20. C2×C4⋊C4×C97 | C22 | semidirect |
| 96. C2×C97 | #399 | semidirect |
| 104. C97 | C2×#399 | semidirect |
| 106. C22×C4⋊C4 | D97 | semidirect |
| 119. C2×C4⋊C4 | C2×D97 | semidirect |
| 201. C2 | #20260670 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095490 | 2 |
| C22×#13095488 | 2 |
| #20260670 | 2 |
| C2×#15690717 | 2 |
| C22×C4⋊C4×C97 | 2 |
| C2×#399 | 97 |