Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 48. #14272338 | Q16 | semidirect |
| 71. C233 | #1591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416566 | 2 |
| #28416562 | 2 |
| C4×#16836584 | 2 |
| #28416187 | 2 |
| #28416167 | 2 |
| C8×#14272338 | 2 |
| Q8⋊C8×C233 | 2 |
| #1591 | 233 |