Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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. C2×#20263351 | C2 | semidirect |
| 2. #27161643 | C2 | semidirect |
| 3. #27161252 | C2 | semidirect |
| 4. #27161247 | C2 | semidirect |
| 5. #27161096 | C2 | semidirect |
| 6. #27161063 | C2 | semidirect |
| 7. #585×C197 | C2 | semidirect |
| 8. C22×D788 | C22 | semidirect |
| 10. #20263351 | C22 | semidirect |
| 13. C2×#15691342 | C22 | semidirect |
| 14. #20263322 | C22 | semidirect |
| 15. #20263315 | C22 | semidirect |
| 18. #20263285 | C22 | semidirect |
| 19. #20263253 | C22 | semidirect |
| 20. #20263245 | C22 | semidirect |
| 21. #20263243 | C22 | semidirect |
| 23. 2−1+4×C197 | C22 | semidirect |
| 26. H(5,𝔽2)×C197 | C22 | semidirect |
| 56. #41×C197 | D4 | semidirect |
| 60. C2×Q8×C197 | D4 | semidirect |
| 68. C2×D4×C197 | D4 | semidirect |
| 134. C197 | #3021 | semidirect |
| 136. #585 | D197 | semidirect |
| 144. 2−1+4 | C2×D197 | semidirect |
| 147. H(5,𝔽2) | C2×D197 | semidirect |
| 177. #41 | C22⋊D197 | semidirect |
| 181. C2×Q8 | C22⋊D197 | semidirect |
| 194. C2×D4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| #27161643 | 2 |
| #27161252 | 2 |
| #27161247 | 2 |
| #27161096 | 2 |
| #27161063 | 2 |
| #585×C197 | 2 |
| #3021 | 197 |