Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 88 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. #15690879 | C4 | semidirect |
| 10. #15690878 | C4 | semidirect |
| 13. C8×#87604 | C4 | semidirect |
| 14. C8×#87604 | C4 | semidirect |
| 17. #15690746 | C4 | semidirect |
| 18. #15690745 | C4 | semidirect |
| 19. #108×C97 | C4 | semidirect |
| 74. C97 | #1772 | semidirect |
| 87. #108 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261745 | 2 |
| #20261701 | 2 |
| C2×C8×#87604 | 2 |
| #20261607 | 2 |
| #108×D97 | 2 |
| #1772 | 97 |