Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 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. #20261464 | C2 | semidirect |
| 4. #20261086 | C2 | semidirect |
| 5. #20261045 | C2 | semidirect |
| 8. #20260945 | C2 | semidirect |
| 9. C8×Dic194 | C2 | semidirect |
| 10. #20260827 | C2 | semidirect |
| 116. C97 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261464 | 2 |
| #20261455 | 2 |
| #20261088 | 2 |
| #20261086 | 2 |
| #20261045 | 2 |
| #20261015 | 2 |
| #20260955 | 2 |
| #20260945 | 2 |
| C8×Dic194 | 2 |
| #20260827 | 2 |
| C4×SD16×C97 | 2 |
| #3364 | 97 |