Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 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. #20261762 | C2 | semidirect |
| 2. #20261752 | C2 | semidirect |
| 3. #20261703 | C2 | semidirect |
| 4. C2×C22⋊#11715897 | C2 | semidirect |
| 6. C2×#13095519 | C22 | semidirect |
| 7. C22×#11715897 | C22 | semidirect |
| 8. #15690877 | C22 | semidirect |
| 9. #15690867 | C22 | semidirect |
| 11. C22⋊#11715897 | C22 | semidirect |
| 12. C4×#11715897 | C22 | semidirect |
| 26. C2×C22⋊D97 | C8 | semidirect |
| 47. C23×C97 | C2×C8 | semidirect |
| 52. C22×D97 | C2×C8 | semidirect |
| 58. C22⋊D97 | C2×C8 | semidirect |
| 63. C2×Dic97 | C2×C8 | semidirect |
| 96. C97 | #2972 | semidirect |
| 147. C23 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261762 | 2 |
| #20261752 | 2 |
| #20261703 | 2 |
| C2×C22⋊#11715897 | 2 |
| C2×#15690770 | 2 |
| #2972 | 97 |