Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #20260487 | C2 | semidirect |
| 5. #20260486 | C2 | semidirect |
| 6. #20260485 | C2 | semidirect |
| 7. #335×C97 | C2 | semidirect |
| 27. #13095494 | C8 | semidirect |
| 56. C8×C97 | C2×C8 | semidirect |
| 60. #11715895 | C2×C8 | semidirect |
| 78. C97 | #1565 | semidirect |
| 83. #335 | D97 | semidirect |
| 138. C8 | C8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260787 | 2 |
| C4⋊C8×D97 | 2 |
| C4×#13095494 | 2 |
| #20260487 | 2 |
| #20260486 | 2 |
| #20260485 | 2 |
| #335×C97 | 2 |
| #1565 | 97 |