Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×#15690727 | C2 | semidirect |
| 4. C2×#15690726 | C2 | semidirect |
| 5. #100×D97 | C2 | direct (N × H) |
| 6. C2×#100×C97 | C2 | semidirect |
| 16. C2×#13095495 | C22 | semidirect |
| 19. M16×D97 | C22 | semidirect |
| 21. #15690727 | C22 | semidirect |
| 22. #15690726 | C22 | semidirect |
| 24. C2×M16×C97 | C22 | semidirect |
| 25. #100×C97 | C22 | semidirect |
| 51. #13095495 | C23 | semidirect |
| 62. M16×C97 | C23 | semidirect |
| 119. C2×D97 | #100 | direct (N × H) |
| 128. C2×C97 | C2×#100 | semidirect |
| 132. D97 | C2×#100 | direct (N × H) |
| 134. C97 | C22×#100 | semidirect |
| 140. C2×#100 | D97 | direct (N × H) |
| 155. C2×M16 | C2×D97 | semidirect |
| 159. #100 | C2×D97 | direct (N × H) |
| 194. M16 | C22×D97 | semidirect |
| 265. C2 | #100×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D97 | 2 |
| C2×M16×D97 | 2 |
| C2×#15690727 | 2 |
| C2×#15690726 | 2 |
| #100×D97 | 2 |
| C2×#100×C97 | 2 |
| C22×#100 | 97 |