Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15690816 | C2 | semidirect |
| 2. #20261302 | C2 | semidirect |
| 3. #20260985 | C2 | semidirect |
| 4. #20260968 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260740 | C2 | semidirect |
| 7. C22×D8×C97 | C2 | semidirect |
| 11. C2×#13095494 | C22 | semidirect |
| 12. C2×C8×D97 | C22 | semidirect |
| 15. #15690781 | C22 | semidirect |
| 18. #15690744 | C22 | semidirect |
| 19. #15690742 | C22 | semidirect |
| 20. #15690731 | C22 | semidirect |
| 49. C2×C8×C97 | D4 | semidirect |
| 94. C97 | #3058 | semidirect |
| 95. C22×D8 | D97 | semidirect |
| 139. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261302 | 2 |
| #20260985 | 2 |
| #20260968 | 2 |
| #20260773 | 2 |
| #20260740 | 2 |
| C22×D8×C97 | 2 |
| #3058 | 97 |