Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 2. C22×#15691335 | C2 | semidirect |
| 3. C22×#15691335 | C2 | semidirect |
| 4. #27160996 | C2 | direct (N × H) |
| 5. C2×#20263233 | C2 | semidirect |
| 6. C22×C4⋊C4×C197 | C2 | semidirect |
| 14. C2×#15691335 | C22 | semidirect |
| 15. C2×#15691335 | C22 | semidirect |
| 16. #20263233 | C22 | semidirect |
| 21. C2×C4⋊C4×C197 | C22 | semidirect |
| 46. C22×C4×C197 | D4 | semidirect |
| 85. C2×C4×C197 | C2×D4 | semidirect |
| 108. C2×C197 | #394 | semidirect |
| 115. C197 | C2×#394 | semidirect |
| 118. C22×C4⋊C4 | D197 | semidirect |
| 132. C2×C4⋊C4 | C2×D197 | semidirect |
| 160. C22×C4 | D788 | semidirect |
| 201. C2×C4 | C2×D788 | semidirect |
| 225. C2 | #27160996 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D788 | 2 |
| C22×#15691335 | 2 |
| #27160996 | 2 |
| C2×#20263233 | 2 |
| C22×C4⋊C4×C197 | 2 |
| C2×#394 | 197 |