Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20260783 | C2 | semidirect |
| 4. C4×#13095495 | C2 | semidirect |
| 5. #20260506 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 14. #15690729 | C4 | semidirect |
| 15. #15690727 | C4 | semidirect |
| 96. C97 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260783 | 2 |
| #20260752 | 2 |
| #20260719 | 2 |
| C4×#13095495 | 2 |
| #20260506 | 2 |
| #20260495 | 2 |
| C2×#104×C97 | 2 |
| #1932 | 97 |