Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic194 | C2 | semidirect |
| 3. #20261082 | C2 | semidirect |
| 4. #20261080 | C2 | semidirect |
| 5. #20261025 | C2 | semidirect |
| 6. #20261024 | C2 | semidirect |
| 7. #20260935 | C2 | semidirect |
| 8. #20260933 | C2 | semidirect |
| 9. C8×Dic194 | C2 | semidirect |
| 10. #20260820 | C2 | semidirect |
| 11. C4×SD16×C97 | C2 | semidirect |
| 77. Q8×C97 | #41 | semidirect |
| 99. Dic194 | SD16 | semidirect |
| 126. C97 | #3362 | semidirect |
| 137. C4×SD16 | D97 | semidirect |
| 206. Q8 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic194 | 2 |
| #20261406 | 2 |
| #20261082 | 2 |
| #20261080 | 2 |
| #20261025 | 2 |
| #20261024 | 2 |
| #20260935 | 2 |
| #20260933 | 2 |
| C8×Dic194 | 2 |
| #20260820 | 2 |
| C4×SD16×C97 | 2 |
| #3362 | 97 |