Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q16×D97 | C2 | semidirect |
| 3. C2×#15690755 | C2 | semidirect |
| 4. C2×#15690754 | C2 | semidirect |
| 5. C2×#15690753 | C2 | semidirect |
| 6. SD32×D97 | C2 | direct (N × H) |
| 7. C2×C16×D97 | C2 | semidirect |
| 8. C2×SD32×C97 | C2 | semidirect |
| 11. C2×Dic388 | C22 | semidirect |
| 14. Q16×D97 | C22 | semidirect |
| 20. #15690755 | C22 | semidirect |
| 21. #15690754 | C22 | semidirect |
| 22. #15690753 | C22 | semidirect |
| 23. C2×#13095486 | C22 | semidirect |
| 24. C16×D97 | C22 | semidirect |
| 25. C2×Q16×C97 | C22 | semidirect |
| 27. SD32×C97 | C22 | semidirect |
| 28. C2×C16×C97 | C22 | semidirect |
| 41. Dic388 | C23 | semidirect |
| 49. #13095486 | C23 | semidirect |
| 53. Q16×C97 | C23 | semidirect |
| 57. C16×C97 | C23 | semidirect |
| 89. C2×D97 | SD32 | direct (N × H) |
| 97. C2×C97 | C2×SD32 | semidirect |
| 100. D97 | C2×SD32 | direct (N × H) |
| 102. C97 | C22×SD32 | semidirect |
| 109. C2×SD32 | D97 | direct (N × H) |
| 117. C2×Q16 | C2×D97 | semidirect |
| 127. SD32 | C2×D97 | direct (N × H) |
| 130. C2×C16 | C2×D97 | semidirect |
| 148. Q16 | C22×D97 | semidirect |
| 159. C16 | C22×D97 | semidirect |
| 201. C2 | SD32×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| C2×D8×D97 | 2 |
| C2×#15690755 | 2 |
| C2×#15690754 | 2 |
| C2×#15690753 | 2 |
| SD32×D97 | 2 |
| C2×C16×D97 | 2 |
| C2×SD32×C97 | 2 |
| C22×SD32 | 97 |