Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
| 4. C2×#15690733 | C2 | semidirect |
| 6. #20260490 | C2 | semidirect |
| 7. #391×C97 | C2 | semidirect |
| 126. C97 | #2015 | semidirect |
| 132. #391 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| C22×#13095498 | 2 |
| C2×#15690798 | 2 |
| C2×#15690733 | 2 |
| C2×#15690730 | 2 |
| #20260490 | 2 |
| #391×C97 | 2 |
| #2015 | 97 |