Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 2. C2×M16×D97 | C2 | semidirect |
| 3. #20260716 | C2 | direct (N × H) |
| 4. C2×#15690728 | C2 | semidirect |
| 5. C2×#15690727 | C2 | semidirect |
| 6. C2×#100×C97 | C2 | semidirect |
| 19. M16×D97 | C22 | semidirect |
| 21. #15690728 | C22 | semidirect |
| 22. #15690727 | C22 | semidirect |
| 25. #100×C97 | C22 | semidirect |
| 116. C2×C97 | #413 | semidirect |
| 120. C97 | C2×#413 | semidirect |
| 126. C2×#100 | D97 | semidirect |
| 145. #100 | C2×D97 | semidirect |
| 237. C2 | #20260716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095510 | 2 |
| C2×M16×D97 | 2 |
| #20260716 | 2 |
| C2×#15690728 | 2 |
| C2×#15690727 | 2 |
| C2×#100×C97 | 2 |
| C2×#413 | 97 |