Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15690832 | C2 | semidirect |
| 2. #20261246 | C2 | semidirect |
| 3. #20260976 | C2 | semidirect |
| 4. #20260971 | C2 | semidirect |
| 5. #20260964 | C2 | semidirect |
| 6. #20260773 | C2 | semidirect |
| 7. #20260732 | C2 | semidirect |
| 8. C23×C8×C97 | C2 | semidirect |
| 11. C2×Dic388 | C22 | semidirect |
| 12. C2×#13095500 | C22 | semidirect |
| 13. C2×D776 | C22 | semidirect |
| 20. #15690744 | C22 | semidirect |
| 21. #15690742 | C22 | semidirect |
| 22. #15690735 | C22 | semidirect |
| 23. #15690732 | C22 | semidirect |
| 56. C2×C8×C97 | D4 | semidirect |
| 91. C22×C97 | #135 | semidirect |
| 107. C97 | #3050 | semidirect |
| 109. C23×C8 | D97 | semidirect |
| 157. C2×C8 | C22⋊D97 | semidirect |
| 200. C22 | #15690832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261246 | 2 |
| #20260976 | 2 |
| #20260971 | 2 |
| #20260964 | 2 |
| #20260773 | 2 |
| #20260732 | 2 |
| C23×C8×C97 | 2 |
| #3050 | 97 |