Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #20261458 | C2 | semidirect |
| 3. #20261140 | C2 | semidirect |
| 4. #20261069 | C2 | semidirect |
| 5. #20261057 | C2 | semidirect |
| 6. #20261020 | C2 | semidirect |
| 7. #20261015 | C2 | semidirect |
| 8. #20260978 | C2 | semidirect |
| 9. #20260814 | C2 | semidirect |
| 10. #20260774 | C2 | semidirect |
| 11. C4×SD16×C97 | C2 | semidirect |
| 98. C8×C97 | #41 | semidirect |
| 123. C97 | #3353 | semidirect |
| 132. C4×SD16 | D97 | semidirect |
| 222. C8 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261390 | 2 |
| #20261140 | 2 |
| #20261069 | 2 |
| #20261057 | 2 |
| #20261020 | 2 |
| #20261015 | 2 |
| #20260978 | 2 |
| #20260814 | 2 |
| #20260774 | 2 |
| C4×SD16×C97 | 2 |
| #3353 | 97 |