Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20261451 | C2 | semidirect |
| 2. #20261388 | C2 | semidirect |
| 3. #20261061 | C2 | semidirect |
| 4. #20261055 | C2 | semidirect |
| 5. #20261022 | C2 | semidirect |
| 6. #20261012 | C2 | semidirect |
| 7. #20260989 | C2 | semidirect |
| 8. C4×D776 | C2 | semidirect |
| 9. #20260814 | C2 | semidirect |
| 10. #20260774 | C2 | semidirect |
| 11. #498×C97 | C2 | semidirect |
| 100. C8×C97 | #41 | semidirect |
| 128. C97 | #3354 | semidirect |
| 131. #498 | D97 | semidirect |
| 229. C8 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261451 | 2 |
| #20261388 | 2 |
| #20261061 | 2 |
| #20261055 | 2 |
| #20261022 | 2 |
| #20261012 | 2 |
| #20260989 | 2 |
| C4×D776 | 2 |
| #20260814 | 2 |
| #20260774 | 2 |
| #498×C97 | 2 |
| #3354 | 97 |