Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 3. #20260557 | C2 | semidirect |
| 4. #20260551 | C2 | semidirect |
| 6. #20260513 | C2 | semidirect |
| 7. #441×C97 | C2 | semidirect |
| 10. #15690756 | C4 | semidirect |
| 11. #15690753 | C4 | semidirect |
| 65. C97 | #2180 | semidirect |
| 68. #441 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261176 | 2 |
| #20260858 | 2 |
| #20260557 | 2 |
| #20260551 | 2 |
| #20260544 | 2 |
| #20260513 | 2 |
| #441×C97 | 2 |
| #2180 | 97 |