Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15690841 | C2 | semidirect |
| 3. C2×#15690816 | C2 | semidirect |
| 4. #20260995 | C2 | direct (N × H) |
| 5. C2×#15690746 | C2 | semidirect |
| 6. C2×#15690729 | C2 | semidirect |
| 7. C2×#15690727 | C2 | semidirect |
| 8. C22×SD16×C97 | C2 | semidirect |
| 11. #15690841 | C22 | semidirect |
| 19. #15690816 | C22 | semidirect |
| 25. #15690746 | C22 | semidirect |
| 26. #15690729 | C22 | semidirect |
| 27. #15690727 | C22 | semidirect |
| 33. C2×SD16×C97 | C22 | semidirect |
| 135. C2×C97 | #471 | semidirect |
| 139. C97 | C2×#471 | semidirect |
| 142. C22×SD16 | D97 | semidirect |
| 161. C2×SD16 | C2×D97 | semidirect |
| 275. C2 | #20260995 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| C2×#15690836 | 2 |
| C2×#15690816 | 2 |
| #20260995 | 2 |
| C2×#15690746 | 2 |
| C2×#15690729 | 2 |
| C2×#15690727 | 2 |
| C22×SD16×C97 | 2 |
| C2×#471 | 97 |