Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. #27161158 | C2 | direct (N × H) |
| 4. C2×C4⋊#13096802 | C2 | semidirect |
| 5. C2×#20263238 | C2 | semidirect |
| 6. C2×C4×C8×C197 | C2 | semidirect |
| 10. C2×#15691341 | C22 | semidirect |
| 16. C4⋊#13096802 | C22 | semidirect |
| 17. #20263238 | C22 | semidirect |
| 21. C4×C8×C197 | C22 | semidirect |
| 39. C2×C8×C197 | D4 | semidirect |
| 57. C2×C4×C197 | M16 | semidirect |
| 65. C8×C197 | C2×D4 | semidirect |
| 76. C4×C197 | C2×M16 | semidirect |
| 80. C2×C197 | #436 | semidirect |
| 85. C197 | C2×#436 | semidirect |
| 92. C2×C4×C8 | D197 | semidirect |
| 107. C4×C8 | C2×D197 | semidirect |
| 123. C2×C8 | D788 | semidirect |
| 142. C2×C4 | #15691341 | semidirect |
| 151. C8 | C2×D788 | semidirect |
| 163. C4 | C2×#15691341 | semidirect |
| 167. C2 | #27161158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691341 | 2 |
| C2×C4×D788 | 2 |
| #27161158 | 2 |
| C2×C4⋊#13096802 | 2 |
| C2×#20263238 | 2 |
| C2×C4×C8×C197 | 2 |
| C2×#436 | 197 |