Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
228 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 5. (C2×#87604)⋊C4 | C4 | semidirect |
| 7. C22×#11715895 | C4 | semidirect |
| 9. C22×C8×C97 | C4 | semidirect |
| 72. C97 | #1289 | semidirect |
| 77. C22×C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261677 | 2 |
| C2×#15690722 | 2 |
| #1289 | 97 |