Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #20261446 | C2 | semidirect |
| 3. #20261078 | C2 | semidirect |
| 4. #20261050 | C2 | semidirect |
| 5. #20261027 | C2 | semidirect |
| 6. #20261022 | C2 | semidirect |
| 7. #20260982 | C2 | semidirect |
| 8. C4×#13095500 | C2 | semidirect |
| 9. #20260814 | C2 | semidirect |
| 10. #20260776 | C2 | semidirect |
| 11. #500×C97 | C2 | semidirect |
| 122. C97 | #3357 | semidirect |
| 125. #500 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261451 | 2 |
| #20261446 | 2 |
| #20261078 | 2 |
| #20261050 | 2 |
| #20261027 | 2 |
| #20261022 | 2 |
| #20260982 | 2 |
| C4×#13095500 | 2 |
| #20260814 | 2 |
| #20260776 | 2 |
| #500×C97 | 2 |
| #3357 | 97 |