Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20261694 | C2 | semidirect |
| 3. C4×C4⋊#87604 | C2 | semidirect |
| 4. #20261608 | C2 | semidirect |
| 9. #15690872 | C4 | semidirect |
| 15. C4×D388 | C4 | semidirect |
| 16. D4×Dic97 | C4 | semidirect |
| 17. #15690772 | C4 | semidirect |
| 23. C4×D4×C97 | C4 | semidirect |
| 26. #13095519 | C2×C4 | semidirect |
| 29. C4⋊#87604 | C2×C4 | semidirect |
| 68. D4×C97 | C42 | semidirect |
| 81. D388 | C42 | semidirect |
| 122. C97 | #1762 | semidirect |
| 136. C4×D4 | #87604 | semidirect |
| 190. D4 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690872 | 2 |
| #20261694 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261608 | 2 |
| C4×D4×D97 | 2 |
| #1762 | 97 |