Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 19. #107×C97 | C4 | semidirect |
| 20. #107×C97 | C4 | semidirect |
| 21. #106×C97 | C4 | semidirect |
| 22. #106×C97 | C4 | semidirect |
| 89. C97 | #1922 | semidirect |
| 104. #107 | Dic97 | semidirect |
| 105. #107 | Dic97 | semidirect |
| 106. #106 | Dic97 | semidirect |
| 107. #106 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260762 | 2 |
| #20260691 | 2 |
| #20260500 | 2 |
| #20260494 | 2 |
| #20260489 | 2 |
| #427×C97 | 2 |
| #1922 | 97 |