Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
820 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 105 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×#15690727 | C2 | semidirect |
| 3. C2×#15690726 | C2 | semidirect |
| 4. #20260698 | C2 | semidirect |
| 5. C2×#100×C97 | C2 | semidirect |
| 14. C2×#13095495 | C22 | semidirect |
| 19. C2×M16×C97 | C22 | semidirect |
| 104. C2×D97 | #100 | semidirect |
| 116. C97 | #1783 | semidirect |
| 120. C2×#100 | D97 | semidirect |
| 132. C2×M16 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D97 | 2 |
| C2×#15690727 | 2 |
| C2×#15690726 | 2 |
| #20260698 | 2 |
| C2×#100×C97 | 2 |
| #1783 | 97 |