Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13095500 | C2 | semidirect |
| 2. C2×#15690789 | C2 | semidirect |
| 4. #20260981 | C2 | direct (N × H) |
| 5. C2×#15690744 | C2 | semidirect |
| 6. C2×#15690735 | C2 | semidirect |
| 7. C2×#15690732 | C2 | semidirect |
| 8. C22×M16×C97 | C2 | semidirect |
| 13. C2×#13095500 | C22 | semidirect |
| 15. #15690789 | C22 | semidirect |
| 23. #15690744 | C22 | semidirect |
| 24. #15690735 | C22 | semidirect |
| 25. #15690732 | C22 | semidirect |
| 28. C2×M16×C97 | C22 | semidirect |
| 62. C2×C8×C97 | D4 | semidirect |
| 97. C8×C97 | C2×D4 | semidirect |
| 118. C2×C97 | #468 | semidirect |
| 124. C97 | C2×#468 | semidirect |
| 126. C22×M16 | D97 | semidirect |
| 140. C2×M16 | C2×D97 | semidirect |
| 179. C2×C8 | C22⋊D97 | semidirect |
| 221. C8 | C2×C22⋊D97 | semidirect |
| 243. C2 | #20260981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C2×#15690789 | 2 |
| C2×#15690784 | 2 |
| #20260981 | 2 |
| C2×#15690744 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| C22×M16×C97 | 2 |
| C2×#468 | 97 |