Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261363 | C2 | semidirect |
| 3. #20261045 | C2 | semidirect |
| 4. #20261034 | C2 | semidirect |
| 5. #20261029 | C2 | semidirect |
| 6. #20261014 | C2 | semidirect |
| 7. C2×#15690743 | C2 | semidirect |
| 8. #20260763 | C2 | semidirect |
| 11. #428×C97 | C2 | semidirect |
| 42. #13095511 | Q8 | semidirect |
| 124. C97 | #3083 | semidirect |
| 131. #428 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261216 | 2 |
| #20261045 | 2 |
| #20261034 | 2 |
| #20261029 | 2 |
| #20261014 | 2 |
| C2×#15690743 | 2 |
| #20260763 | 2 |
| #20260737 | 2 |
| #20260729 | 2 |
| #428×C97 | 2 |
| #3083 | 97 |