Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20261131 | C2 | semidirect |
| 2. #20261114 | C2 | semidirect |
| 6. #20260456 | C2 | semidirect |
| 7. #487×C97 | C2 | semidirect |
| 69. C97 | #1720 | semidirect |
| 72. #487 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261131 | 2 |
| #20261114 | 2 |
| #20261083 | 2 |
| #20261082 | 2 |
| #20260456 | 2 |
| #487×C97 | 2 |
| #1720 | 97 |