Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20261283 | C2 | semidirect |
| 2. C4×#13095512 | C2 | semidirect |
| 3. #20261057 | C2 | semidirect |
| 4. #20261020 | C2 | semidirect |
| 5. #20261016 | C2 | semidirect |
| 6. #20260927 | C2 | semidirect |
| 7. #20260879 | C2 | semidirect |
| 8. #20260844 | C2 | semidirect |
| 9. #20260836 | C2 | semidirect |
| 10. #20260791 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 87. Q8×C97 | #41 | semidirect |
| 106. D388 | #41 | semidirect |
| 145. C97 | #3115 | semidirect |
| 151. #460 | D97 | semidirect |
| 233. Q8 | #13095510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261283 | 2 |
| C4×#13095512 | 2 |
| #20261057 | 2 |
| #20261020 | 2 |
| #20261016 | 2 |
| #20260927 | 2 |
| #20260879 | 2 |
| #20260844 | 2 |
| #20260836 | 2 |
| #20260791 | 2 |
| #460×C97 | 2 |
| #3115 | 97 |