Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 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×#13095501 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. C22×#13095498 | C2 | semidirect |
| 5. C2×#15690798 | C2 | semidirect |
| 6. #20261117 | C2 | direct (N × H) |
| 7. C2×C4×#11715895 | C2 | semidirect |
| 8. C2×#124×C97 | C2 | semidirect |
| 12. C2×#13095501 | C22 | semidirect |
| 14. C2×#13095499 | C22 | semidirect |
| 16. C2×#13095498 | C22 | semidirect |
| 22. #15690798 | C22 | semidirect |
| 24. C4×#11715895 | C22 | semidirect |
| 28. #124×C97 | C22 | semidirect |
| 112. C2×C97 | #495 | semidirect |
| 117. C97 | C2×#495 | semidirect |
| 123. C2×#124 | D97 | semidirect |
| 143. #124 | C2×D97 | semidirect |
| 230. C2 | #20261117 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| C22×#13095499 | 2 |
| C22×#13095498 | 2 |
| C22×#13095496 | 2 |
| C2×#15690798 | 2 |
| #20261117 | 2 |
| C2×C4×#11715895 | 2 |
| C2×#124×C97 | 2 |
| C2×#495 | 97 |