Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
262 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #20260783 | C2 | semidirect |
| 3. #20260758 | C2 | semidirect |
| 5. #20260505 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 17. #15690737 | C4 | semidirect |
| 18. #15690737 | C4 | semidirect |
| 98. C97 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261502 | 2 |
| #20260783 | 2 |
| #20260758 | 2 |
| C2×#15690737 | 2 |
| #20260505 | 2 |
| #20260494 | 2 |
| #421×C97 | 2 |
| #1861 | 97 |