Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #20260753 | C2 | semidirect |
| 3. #20260743 | C2 | semidirect |
| 4. #20260719 | C2 | semidirect |
| 5. #410×C97 | C2 | semidirect |
| 8. C2×#13095511 | C4 | semidirect |
| 12. C22×Dic194 | C4 | semidirect |
| 109. C97 | #1796 | semidirect |
| 114. #410 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| #20260753 | 2 |
| #20260743 | 2 |
| #20260719 | 2 |
| #410×C97 | 2 |
| #1796 | 97 |