Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#15690755 | C2 | semidirect |
| 3. C2×#15690754 | C2 | semidirect |
| 4. #20260977 | C2 | semidirect |
| 5. #20260535 | C2 | semidirect |
| 6. #20260514 | C2 | semidirect |
| 7. #357×C97 | C2 | semidirect |
| 9. C2×Dic388 | C22 | semidirect |
| 18. C2×#13095486 | C22 | semidirect |
| 21. C2×C16×C97 | C22 | semidirect |
| 22. #107×C97 | C22 | semidirect |
| 79. C2×D97 | SD32 | semidirect |
| 92. C97 | #2187 | semidirect |
| 98. #357 | D97 | semidirect |
| 112. C2×C16 | C2×D97 | semidirect |
| 113. #107 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D97 | 2 |
| C2×#15690755 | 2 |
| C2×#15690754 | 2 |
| #20260977 | 2 |
| #20260535 | 2 |
| #20260514 | 2 |
| #357×C97 | 2 |
| #2187 | 97 |