Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #20261698 | C2 | semidirect |
| 4. #20261617 | C2 | semidirect |
| 8. #15690871 | C4 | semidirect |
| 9. #15690870 | C4 | semidirect |
| 17. C2×#13095495 | C4 | semidirect |
| 18. C2×#13095494 | C4 | semidirect |
| 20. C2×C8×D97 | C4 | semidirect |
| 22. C22×C8×C97 | C4 | semidirect |
| 94. C97 | #1757 | semidirect |
| 109. C22×C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261721 | 2 |
| #20261714 | 2 |
| #20261698 | 2 |
| #20261617 | 2 |
| C2×#15690816 | 2 |
| #1757 | 97 |