Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20260486 | C2 | semidirect |
| 4. #20260485 | C2 | semidirect |
| 5. #334×C97 | C2 | semidirect |
| 46. C8×C97 | M16 | semidirect |
| 49. #11715895 | M16 | semidirect |
| 66. C97 | #1566 | semidirect |
| 71. #334 | D97 | semidirect |
| 115. C8 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260757 | 2 |
| C4×C8×D97 | 2 |
| #20260486 | 2 |
| #20260485 | 2 |
| #334×C97 | 2 |
| #1566 | 97 |