Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 9. #15690864 | C4 | semidirect |
| 10. C4×#11715897 | C4 | semidirect |
| 11. C8×#87604 | C4 | semidirect |
| 15. #15690721 | C4 | semidirect |
| 16. #15690720 | C4 | semidirect |
| 17. #97×C97 | C4 | semidirect |
| 61. C97 | #1726 | semidirect |
| 75. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690864 | 2 |
| C4×#13095519 | 2 |
| C2×C8×#87604 | 2 |
| #20261671 | 2 |
| #97×D97 | 2 |
| #1726 | 97 |