Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
150 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 18. C22×C4×C97 | C8 | semidirect |
| 55. C97 | #1317 | semidirect |
| 70. C22×C4 | #11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261578 | 2 |
| #20260598 | 2 |
| #1317 | 97 |