Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 8. #15690881 | C4 | semidirect |
| 9. #15690880 | C4 | semidirect |
| 10. #15690879 | C4 | semidirect |
| 11. #15690878 | C4 | semidirect |
| 17. #15690721 | C4 | semidirect |
| 18. #15690720 | C4 | semidirect |
| 19. #15690720 | C4 | semidirect |
| 20. #97×C97 | C4 | semidirect |
| 76. C97 | #1773 | semidirect |
| 95. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#108 | 2 |
| #20261745 | 2 |
| #20261698 | 2 |
| #20261606 | 2 |
| #97×D97 | 2 |
| #1773 | 97 |