Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261455 | C2 | semidirect |
| 3. #20261140 | C2 | semidirect |
| 4. #20261071 | C2 | semidirect |
| 5. #20261060 | C2 | semidirect |
| 6. #20261021 | C2 | semidirect |
| 7. #20261016 | C2 | semidirect |
| 8. #20260981 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. #20260777 | C2 | semidirect |
| 11. #436×C97 | C2 | semidirect |
| 99. C8×C97 | #41 | semidirect |
| 123. C97 | #3353 | semidirect |
| 133. #436 | D97 | semidirect |
| 222. C8 | #13095510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261455 | 2 |
| #20261389 | 2 |
| #20261140 | 2 |
| #20261071 | 2 |
| #20261060 | 2 |
| #20261021 | 2 |
| #20261016 | 2 |
| #20260981 | 2 |
| C4×#13095500 | 2 |
| #20260777 | 2 |
| #436×C97 | 2 |
| #3353 | 97 |