Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 6. C2×C4×#87604 | C4 | semidirect |
| 7. #15690867 | C4 | semidirect |
| 13. #15690717 | C4 | semidirect |
| 14. #95×C97 | C4 | semidirect |
| 87. C97 | #1284 | semidirect |
| 101. #95 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261706 | 2 |
| C4×C22⋊#87604 | 2 |
| #20260597 | 2 |
| #1284 | 97 |