Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#15690873 | C2 | semidirect |
| 3. C4×#13095519 | C2 | semidirect |
| 4. #20261679 | C2 | semidirect |
| 14. #15690799 | C4 | semidirect |
| 15. #15690798 | C4 | semidirect |
| 16. #15690797 | C4 | semidirect |
| 20. #124×C97 | C4 | semidirect |
| 98. C97 | #1958 | semidirect |
| 111. #124 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690873 | 2 |
| C2×#15690872 | 2 |
| C4×#13095519 | 2 |
| #20261679 | 2 |
| #124×D97 | 2 |
| #1958 | 97 |