Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20261548 | C2 | semidirect |
| 2. #20261177 | C2 | semidirect |
| 3. #20261176 | C2 | semidirect |
| 4. #20261168 | C2 | semidirect |
| 5. #20261167 | C2 | semidirect |
| 6. Q32×D97 | C2 | semidirect |
| 7. #20261151 | C2 | semidirect |
| 8. C2×Q32×C97 | C2 | semidirect |
| 82. C97 | #3417 | semidirect |
| 89. C2×Q32 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261548 | 2 |
| #20261177 | 2 |
| #20261176 | 2 |
| #20261168 | 2 |
| #20261167 | 2 |
| Q32×D97 | 2 |
| #20261151 | 2 |
| C2×Q32×C97 | 2 |
| #3417 | 97 |