Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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×#15691359 | C2 | semidirect |
| 2. #27161630 | C2 | direct (N × H) |
| 3. C2×#20263323 | C2 | semidirect |
| 4. C2×#20263315 | C2 | semidirect |
| 5. C2×#20263301 | C2 | semidirect |
| 6. C2×#20263288 | C2 | semidirect |
| 7. C2×C42×D197 | C2 | semidirect |
| 8. C2×C4⋊Q8×C197 | C2 | semidirect |
| 10. C2×#15691359 | C22 | semidirect |
| 17. #20263323 | C22 | semidirect |
| 18. #20263315 | C22 | semidirect |
| 19. #20263301 | C22 | semidirect |
| 20. #20263288 | C22 | semidirect |
| 24. C42×D197 | C22 | semidirect |
| 26. C4⋊Q8×C197 | C22 | semidirect |
| 42. C2×C4×D197 | D4 | semidirect |
| 71. C4×D197 | C2×D4 | semidirect |
| 76. C2×C4×C197 | #41 | semidirect |
| 91. C4×C197 | C2×#41 | semidirect |
| 94. C2×C197 | #532 | semidirect |
| 99. C197 | C2×#532 | semidirect |
| 103. C2×C4⋊Q8 | D197 | semidirect |
| 118. C4⋊Q8 | C2×D197 | semidirect |
| 176. C2×C4 | #15691359 | semidirect |
| 193. C4 | C2×#15691359 | semidirect |
| 196. C2 | #27161630 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691359 | 2 |
| #27161630 | 2 |
| C2×#20263323 | 2 |
| C2×#20263315 | 2 |
| C2×#20263301 | 2 |
| C2×#20263288 | 2 |
| C2×C42×D197 | 2 |
| C2×C4⋊Q8×C197 | 2 |
| C2×#532 | 197 |