Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
| 5. #20260507 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 7. C4×M16×C97 | C2 | semidirect |
| 16. #15690728 | C4 | semidirect |
| 17. #15690726 | C4 | semidirect |
| 96. C97 | #1932 | semidirect |
| 101. C4×M16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260783 | 2 |
| #20260751 | 2 |
| C2×#15690738 | 2 |
| #20260717 | 2 |
| #20260507 | 2 |
| #20260495 | 2 |
| C4×M16×C97 | 2 |
| #1932 | 97 |