Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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. #20260772 | C2 | direct (N × H) |
| 4. C2×#15690744 | C2 | semidirect |
| 5. C2×#15690741 | C2 | semidirect |
| 6. C2×#107×C97 | C2 | semidirect |
| 9. C2×C8×D97 | C4 | semidirect |
| 16. #15690744 | C22 | semidirect |
| 17. #15690741 | C22 | semidirect |
| 20. #107×C97 | C22 | semidirect |
| 30. C8×D97 | C2×C4 | semidirect |
| 75. C2×C97 | #427 | semidirect |
| 81. C97 | C2×#427 | semidirect |
| 86. C2×#107 | D97 | semidirect |
| 100. #107 | C2×D97 | semidirect |
| 157. C2 | #20260772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D97 | 2 |
| C2×#15690768 | 2 |
| #20260772 | 2 |
| C2×#15690744 | 2 |
| C2×#15690741 | 2 |
| C2×#107×C97 | 2 |
| C2×#427 | 97 |