Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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. #28416160 | C2 | semidirect |
| 52. C2×Dic233 | M16 | semidirect |
| 94. C233 | #1463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16836573 | 2 |
| #28416399 | 2 |
| #28416160 | 2 |
| #407×C233 | 2 |
| #1463 | 233 |