Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
584 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 584 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. C22×#15691345 | C2 | semidirect |
| 3. C2×Q8×Dic197 | C2 | semidirect |
| 4. #27161277 | C2 | direct (N × H) |
| 5. C2×#20263255 | C2 | semidirect |
| 6. C2×#20263248 | C2 | semidirect |
| 7. C2×#20263247 | C2 | semidirect |
| 8. C22×SD16×C197 | C2 | semidirect |
| 13. C2×#15691345 | C22 | semidirect |
| 18. Q8×Dic197 | C22 | semidirect |
| 23. #20263255 | C22 | semidirect |
| 24. #20263248 | C22 | semidirect |
| 25. #20263247 | C22 | semidirect |
| 29. C2×SD16×C197 | C22 | semidirect |
| 55. C2×Q8×C197 | D4 | semidirect |
| 78. C2×Dic197 | SD16 | semidirect |
| 89. Q8×C197 | C2×D4 | semidirect |
| 118. Dic197 | C2×SD16 | semidirect |
| 120. C2×C197 | #460 | semidirect |
| 125. C197 | C2×#460 | semidirect |
| 128. C22×SD16 | D197 | semidirect |
| 143. C2×SD16 | C2×D197 | semidirect |
| 161. C2×Q8 | C22⋊D197 | semidirect |
| 203. Q8 | C2×C22⋊D197 | semidirect |
| 247. C2 | #27161277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691345 | 2 |
| C2×#20263322 | 2 |
| C2×Q8×Dic197 | 2 |
| #27161277 | 2 |
| C2×#20263255 | 2 |
| C2×#20263248 | 2 |
| C2×#20263247 | 2 |
| C22×SD16×C197 | 2 |
| C2×#460 | 197 |