Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 11. #15690721 | C4 | semidirect |
| 12. C8×Dic97 | C4 | semidirect |
| 13. C8×Dic97 | C4 | semidirect |
| 14. #97×C97 | C4 | semidirect |
| 59. C97 | #1841 | semidirect |
| 71. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261617 | 2 |
| #20261606 | 2 |
| #20261604 | 2 |
| #20261603 | 2 |
| #20260687 | 2 |
| #1841 | 97 |