Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1144 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #20260598 | C2 | semidirect |
| 4. #20260597 | C2 | semidirect |
| 5. #20260596 | C2 | semidirect |
| 6. #95×D97 | C2 | semidirect |
| 7. #381×C97 | C2 | semidirect |
| 11. C22×C4×D97 | C4 | semidirect |
| 18. #15690717 | C22 | semidirect |
| 19. #15690717 | C22 | semidirect |
| 22. #95×C97 | C22 | semidirect |
| 29. C22×Dic97 | C2×C4 | semidirect |
| 38. C2×C4×D97 | C2×C4 | semidirect |
| 43. C22×C4×C97 | C2×C4 | semidirect |
| 95. D97 | #381 | direct (N × H) |
| 97. C97 | C2×#381 | semidirect |
| 103. #381 | D97 | direct (N × H) |
| 119. #95 | C2×D97 | semidirect |
| 138. C22×C4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D97 | 2 |
| C2×C22⋊C4×D97 | 2 |
| #20260598 | 2 |
| #20260597 | 2 |
| #20260596 | 2 |
| #95×D97 | 2 |
| #381×C97 | 2 |
| C2×#381 | 97 |