Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261131 | C2 | semidirect |
| 3. #20261073 | C2 | semidirect |
| 4. #20261065 | C2 | semidirect |
| 5. #20261027 | C2 | semidirect |
| 6. #20261020 | C2 | semidirect |
| 7. #20260991 | C2 | semidirect |
| 8. C4×#13095501 | C2 | semidirect |
| 10. #20260775 | C2 | semidirect |
| 117. C97 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261455 | 2 |
| #20261131 | 2 |
| #20261073 | 2 |
| #20261065 | 2 |
| #20261027 | 2 |
| #20261020 | 2 |
| #20260991 | 2 |
| C4×#13095501 | 2 |
| #20260813 | 2 |
| #20260775 | 2 |
| #554×C97 | 2 |
| #3356 | 97 |