Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20261536 | C2 | semidirect |
| 2. #20261171 | C2 | semidirect |
| 3. #20261169 | C2 | semidirect |
| 4. #20261167 | C2 | semidirect |
| 5. #20261164 | C2 | semidirect |
| 6. D16×D97 | C2 | semidirect |
| 7. #20261151 | C2 | semidirect |
| 8. C2×D16×C97 | C2 | semidirect |
| 12. #15690832 | C22 | semidirect |
| 13. #15690829 | C22 | semidirect |
| 14. D8×D97 | C22 | semidirect |
| 16. Dic776 | C22 | semidirect |
| 17. #15690755 | C22 | semidirect |
| 18. #15690754 | C22 | semidirect |
| 19. D1552 | C22 | semidirect |
| 20. #15690751 | C22 | semidirect |
| 21. #15690750 | C22 | semidirect |
| 22. #15690749 | C22 | semidirect |
| 23. C16×D97 | C22 | semidirect |
| 24. C2×D8×C97 | C22 | semidirect |
| 25. D16×C97 | C22 | semidirect |
| 26. D16×C97 | C22 | semidirect |
| 27. C2×C16×C97 | C22 | semidirect |
| 85. C97 | #3415 | semidirect |
| 92. C2×D16 | D97 | semidirect |
| 100. C2×D8 | C2×D97 | semidirect |
| 107. D16 | C2×D97 | semidirect |
| 108. D16 | C2×D97 | semidirect |
| 112. C2×C16 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261536 | 2 |
| #20261171 | 2 |
| #20261169 | 2 |
| #20261167 | 2 |
| #20261164 | 2 |
| D16×D97 | 2 |
| #20261151 | 2 |
| C2×D16×C97 | 2 |
| #3415 | 97 |