Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. #20261742 | C2 | semidirect |
| 4. C2×C8×#87604 | C2 | semidirect |
| 5. #20261611 | C2 | semidirect |
| 6. #20261605 | C2 | semidirect |
| 21. #15690734 | C4 | semidirect |
| 22. #15690732 | C4 | semidirect |
| 23. #15690730 | C4 | semidirect |
| 24. #103×C97 | C4 | semidirect |
| 106. C97 | #1937 | semidirect |
| 125. #103 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261742 | 2 |
| C2×#15690875 | 2 |
| #20261710 | 2 |
| C2×C8×#87604 | 2 |
| #20261611 | 2 |
| #20261605 | 2 |
| #20260730 | 2 |
| #1937 | 97 |