Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
752 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #20260742 | C2 | direct (N × H) |
| 5. C2×#15690735 | C2 | semidirect |
| 6. C2×#15690734 | C2 | semidirect |
| 7. C2×#15690733 | C2 | semidirect |
| 8. C2×#103×C97 | C2 | semidirect |
| 13. C2×Q8×D97 | C4 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690734 | C22 | semidirect |
| 27. #15690733 | C22 | semidirect |
| 31. #103×C97 | C22 | semidirect |
| 41. Q8×D97 | C2×C4 | semidirect |
| 117. C2×C97 | #419 | semidirect |
| 123. C97 | C2×#419 | semidirect |
| 131. C2×#103 | D97 | semidirect |
| 154. #103 | C2×D97 | semidirect |
| 241. C2 | #20260742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D97 | 2 |
| C22×#13095494 | 2 |
| C2×#15690768 | 2 |
| #20260742 | 2 |
| C2×#15690735 | 2 |
| C2×#15690734 | 2 |
| C2×#15690733 | 2 |
| C2×#103×C97 | 2 |
| C2×#419 | 97 |