Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×D776 | C2 | semidirect |
| 3. #20260562 | C2 | semidirect |
| 4. #20260536 | C2 | semidirect |
| 5. #20260535 | C2 | semidirect |
| 6. #20260511 | C2 | semidirect |
| 7. C4×D8×C97 | C2 | semidirect |
| 10. #15690751 | C4 | semidirect |
| 23. D776 | C2×C4 | semidirect |
| 27. #13095486 | C2×C4 | semidirect |
| 31. D8×C97 | C2×C4 | semidirect |
| 72. C97 | #2177 | semidirect |
| 75. C4×D8 | D97 | semidirect |
| 99. D8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690751 | 2 |
| C4×D776 | 2 |
| #20260562 | 2 |
| #20260536 | 2 |
| #20260535 | 2 |
| #20260511 | 2 |
| C4×D8×C97 | 2 |
| #2177 | 97 |