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. #20261450 | C2 | semidirect |
| 2. #20261390 | C2 | semidirect |
| 3. #20261133 | C2 | semidirect |
| 4. #20261058 | C2 | semidirect |
| 5. #20261052 | C2 | semidirect |
| 6. #20261025 | C2 | semidirect |
| 7. #20261015 | C2 | semidirect |
| 8. #20260985 | C2 | semidirect |
| 9. #20260814 | C2 | semidirect |
| 10. #20260776 | C2 | semidirect |
| 11. C4×D8×C97 | C2 | semidirect |
| 100. C8×C97 | #41 | semidirect |
| 128. C97 | #3354 | semidirect |
| 137. C4×D8 | D97 | semidirect |
| 229. C8 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261450 | 2 |
| #20261390 | 2 |
| #20261133 | 2 |
| #20261058 | 2 |
| #20261052 | 2 |
| #20261025 | 2 |
| #20261015 | 2 |
| #20260985 | 2 |
| #20260814 | 2 |
| #20260776 | 2 |
| C4×D8×C97 | 2 |
| #3354 | 97 |