Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261458 | C2 | semidirect |
| 2. #20261445 | C2 | semidirect |
| 3. #20261090 | C2 | semidirect |
| 4. #20261086 | C2 | semidirect |
| 5. #20261043 | C2 | semidirect |
| 6. #20261026 | C2 | semidirect |
| 8. #20260941 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 11. C8×Q8×C97 | C2 | semidirect |
| 121. C97 | #3360 | semidirect |
| 130. C8×Q8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261445 | 2 |
| #20261090 | 2 |
| #20261086 | 2 |
| #20261043 | 2 |
| #20261026 | 2 |
| #20260951 | 2 |
| #20260941 | 2 |
| C4×#13095500 | 2 |
| C4×D776 | 2 |
| C8×Q8×C97 | 2 |
| #3360 | 97 |