Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261463 | C2 | semidirect |
| 3. #20261086 | C2 | semidirect |
| 4. #20261084 | C2 | semidirect |
| 5. #20261020 | C2 | semidirect |
| 6. #20261019 | C2 | semidirect |
| 9. C8×Dic194 | C2 | semidirect |
| 95. Dic194 | SD16 | semidirect |
| 119. C97 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261463 | 2 |
| D4×Dic194 | 2 |
| #20261086 | 2 |
| #20261084 | 2 |
| #20261020 | 2 |
| #20261019 | 2 |
| #20260940 | 2 |
| #20260938 | 2 |
| C8×Dic194 | 2 |
| #20260826 | 2 |
| C4×SD16×C97 | 2 |
| #3359 | 97 |