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. #20261699 | C2 | semidirect |
| 4. #20261616 | C2 | semidirect |
| 8. C2×#13095521 | C4 | semidirect |
| 9. C2×#13095520 | C4 | semidirect |
| 12. C2×#13095519 | C4 | semidirect |
| 13. C22×#11715897 | C4 | semidirect |
| 15. #15690871 | C4 | semidirect |
| 16. #15690870 | C4 | semidirect |
| 98. C97 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690897 | 2 |
| #20261722 | 2 |
| #20261699 | 2 |
| #20261616 | 2 |
| #20260707 | 2 |
| #1757 | 97 |