Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#20263322 | C2 | semidirect |
| 3. #27161247 | C2 | direct (N × H) |
| 4. C2×#20263253 | C2 | semidirect |
| 5. C2×#20263243 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C197 | C2 | semidirect |
| 7. C22×D788 | C22 | semidirect |
| 10. #20263351 | C22 | semidirect |
| 13. C2×#15691342 | C22 | semidirect |
| 15. #20263322 | C22 | semidirect |
| 16. C2×C4×Dic197 | C22 | semidirect |
| 17. #20263253 | C22 | semidirect |
| 18. #20263243 | C22 | semidirect |
| 21. H(5,𝔽2)×C197 | C22 | semidirect |
| 31. C2×D788 | C23 | semidirect |
| 38. #15691342 | C23 | semidirect |
| 41. C4×Dic197 | C23 | semidirect |
| 48. #41×C197 | D4 | semidirect |
| 50. C2×Q8×C197 | D4 | semidirect |
| 60. C2×D4×C197 | D4 | semidirect |
| 84. Q8×C197 | C2×D4 | semidirect |
| 91. D4×C197 | C2×D4 | semidirect |
| 123. C2×C197 | #453 | semidirect |
| 126. C197 | C2×#453 | semidirect |
| 128. C2×H(5,𝔽2) | D197 | semidirect |
| 136. H(5,𝔽2) | C2×D197 | semidirect |
| 161. #41 | C22⋊D197 | semidirect |
| 163. C2×Q8 | C22⋊D197 | semidirect |
| 179. C2×D4 | C22⋊D197 | semidirect |
| 205. Q8 | C2×C22⋊D197 | semidirect |
| 215. D4 | C2×C22⋊D197 | semidirect |
| 251. C2 | #27161247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C2×#20263322 | 2 |
| #27161247 | 2 |
| C2×#20263253 | 2 |
| C2×#20263243 | 2 |
| C2×H(5,𝔽2)×C197 | 2 |
| C2×#453 | 197 |