Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 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 |
|---|---|---|
| 1. C2×#15690753 | C2 | semidirect |
| 2. C2×D1552 | C2 | semidirect |
| 3. C2×#15690751 | C2 | semidirect |
| 4. #20261120 | C2 | semidirect |
| 5. #20261110 | C2 | semidirect |
| 6. #20260510 | C2 | semidirect |
| 7. C2×SD32×C97 | C2 | semidirect |
| 35. #13095486 | D4 | semidirect |
| 43. C16×C97 | D4 | semidirect |
| 79. C97 | #2250 | semidirect |
| 81. C2×SD32 | D97 | semidirect |
| 122. C16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| C2×D1552 | 2 |
| C2×#15690751 | 2 |
| #20261120 | 2 |
| #20261110 | 2 |
| #20260510 | 2 |
| C2×SD32×C97 | 2 |
| #2250 | 97 |