Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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. #28416185 | C2 | semidirect |
| 32. #14272338 | M16 | semidirect |
| 60. C233 | #1566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416459 | 2 |
| C2×C4×#14272338 | 2 |
| #28416185 | 2 |
| #423×C233 | 2 |
| #1566 | 233 |