Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20261133 | C2 | semidirect |
| 4. #20261074 | C2 | semidirect |
| 5. #20261064 | C2 | semidirect |
| 6. #20261030 | C2 | semidirect |
| 7. #20261020 | C2 | semidirect |
| 8. #20260990 | C2 | semidirect |
| 10. #20260776 | C2 | semidirect |
| 11. C4×Q16×C97 | C2 | semidirect |
| 117. C97 | #3356 | semidirect |
| 126. C4×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261445 | 2 |
| #20261133 | 2 |
| #20261074 | 2 |
| #20261064 | 2 |
| #20261030 | 2 |
| #20261020 | 2 |
| #20260990 | 2 |
| #20260814 | 2 |
| #20260776 | 2 |
| C4×Q16×C97 | 2 |
| #3356 | 97 |