Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20261701 | C2 | semidirect |
| 4. #20261618 | C2 | semidirect |
| 8. C2×#13095521 | C4 | semidirect |
| 10. C2×#13095519 | C4 | semidirect |
| 18. #15690729 | C4 | semidirect |
| 19. #15690726 | C4 | semidirect |
| 20. #101×C97 | C4 | semidirect |
| 78. C97 | #1757 | semidirect |
| 94. #101 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| #20261716 | 2 |
| #20261701 | 2 |
| #20261618 | 2 |
| #20260718 | 2 |
| #1757 | 97 |