Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 156 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. #20261767 | C2 | semidirect |
| 2. #20261756 | C2 | semidirect |
| 3. #20261705 | C2 | semidirect |
| 4. #20261703 | C2 | semidirect |
| 6. C2×#13095520 | C22 | semidirect |
| 7. C2×#13095519 | C22 | semidirect |
| 8. C4⋊#11715897 | C22 | semidirect |
| 9. #15690867 | C22 | semidirect |
| 11. C22⋊#11715897 | C22 | semidirect |
| 12. #15690865 | C22 | semidirect |
| 52. C22×D97 | M16 | semidirect |
| 96. C97 | #2973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261767 | 2 |
| #20261756 | 2 |
| #20261705 | 2 |
| #20261703 | 2 |
| C2×#15690770 | 2 |
| #2973 | 97 |