Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 1. D353⋊M16 | C2 | semidirect |
| 2. #26015053 | C2 | semidirect |
| 3. #26015052 | C2 | semidirect |
| 52. C353 | #413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D353⋊M16 | 2 |
| #26015053 | 2 |
| #26015052 | 2 |
| C2×#19150737 | 2 |
| #413 | 353 |