Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 3. #20260693 | C2 | semidirect |
| 4. #20260507 | C2 | semidirect |
| 8. C2×#13095495 | C4 | semidirect |
| 10. C22×#11715895 | C4 | semidirect |
| 18. #101×C97 | C4 | semidirect |
| 19. #100×C97 | C4 | semidirect |
| 75. C97 | #1757 | semidirect |
| 90. #101 | Dic97 | semidirect |
| 91. #100 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| #20260709 | 2 |
| #20260693 | 2 |
| #20260507 | 2 |
| #413×C97 | 2 |
| #1757 | 97 |