Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×#15691341 | C2 | semidirect |
| 3. C2×C22⋊#13096802 | C2 | semidirect |
| 4. C2×#20263238 | C2 | semidirect |
| 5. #27160833 | C2 | semidirect |
| 6. #27160833 | C2 | semidirect |
| 7. C2×C22⋊C8×C197 | C2 | semidirect |
| 46. C2×#13096802 | D4 | semidirect |
| 66. C2×C8×C197 | D4 | semidirect |
| 83. C2×Dic197 | M16 | semidirect |
| 96. C23×C197 | M16 | semidirect |
| 151. C197 | #1870 | semidirect |
| 157. C2×C22⋊C8 | D197 | semidirect |
| 213. C2×C8 | C22⋊D197 | semidirect |
| 232. C23 | #15691341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691341 | 2 |
| C2×C4×C22⋊D197 | 2 |
| C2×C22⋊#13096802 | 2 |
| C2×#20263238 | 2 |
| #27160833 | 2 |
| C2×C22⋊C8×C197 | 2 |
| #1870 | 197 |