Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20260635 | C2 | semidirect |
| 3. #20260626 | C2 | semidirect |
| 4. #20260618 | C2 | semidirect |
| 5. #20260613 | C2 | semidirect |
| 6. #20260611 | C2 | semidirect |
| 7. #20260598 | C2 | semidirect |
| 8. C4×#13095488 | C2 | semidirect |
| 9. C4×C22⋊C4×C97 | C2 | semidirect |
| 13. #15690784 | C4 | semidirect |
| 38. C2×C22⋊D97 | C2×C4 | semidirect |
| 45. C4⋊Dic97 | C2×C4 | semidirect |
| 52. #13095488 | C2×C4 | semidirect |
| 57. C22×C4×C97 | C2×C4 | semidirect |
| 135. C97 | #2333 | semidirect |
| 144. C4×C22⋊C4 | D97 | semidirect |
| 183. C22×C4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690784 | 2 |
| #20260635 | 2 |
| #20260626 | 2 |
| #20260618 | 2 |
| #20260613 | 2 |
| #20260611 | 2 |
| #20260598 | 2 |
| C4×#13095488 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #2333 | 97 |