Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
752 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 210 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. #20261728 | C2 | direct (N × H) |
| 4. C2×#15690873 | C2 | semidirect |
| 16. #15690873 | C22 | semidirect |
| 18. C22×Dic194 | C4 | semidirect |
| 23. C2×Q8×D97 | C4 | semidirect |
| 24. C2×Q8×D97 | C4 | semidirect |
| 29. C22×Q8×C97 | C4 | semidirect |
| 48. C2×Dic194 | C2×C4 | semidirect |
| 57. Q8×D97 | C2×C4 | semidirect |
| 76. C2×Q8×C97 | C2×C4 | semidirect |
| 142. C2×C97 | #419 | semidirect |
| 145. D97 | #419 | semidirect |
| 148. C97 | C2×#419 | semidirect |
| 164. C22×Q8 | #87604 | semidirect |
| 200. C2×Q8 | C2×#87604 | semidirect |
| 293. C2 | #20261728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C2×#15690889 | 2 |
| #20261728 | 2 |
| C2×#15690873 | 2 |
| C22×Q8×D97 | 2 |
| C2×#419 | 97 |