Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 3. #20260486 | C2 | semidirect |
| 4. #20260484 | C2 | semidirect |
| 5. #500×C97 | C2 | semidirect |
| 59. C97 | #1695 | semidirect |
| 60. #500 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261022 | 2 |
| #20260814 | 2 |
| #20260486 | 2 |
| #20260484 | 2 |
| #500×C97 | 2 |
| #1695 | 97 |