Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
774 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 204 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×#15690898 | C2 | semidirect |
| 2. #20261709 | C2 | semidirect |
| 3. #20261706 | C2 | semidirect |
| 4. #20261703 | C2 | semidirect |
| 7. C2×#13095521 | C22 | semidirect |
| 8. C2×#13095519 | C22 | semidirect |
| 11. C22⋊#11715897 | C22 | semidirect |
| 12. C22⋊#11715897 | C22 | semidirect |
| 77. C2×D97 | #131 | semidirect |
| 89. C97 | #2880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| #20261709 | 2 |
| #20261706 | 2 |
| #20261703 | 2 |
| C2×#41×D97 | 2 |
| #2880 | 97 |