Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#20263254 | C2 | semidirect |
| 3. #27161081 | C2 | semidirect |
| 4. #27161080 | C2 | semidirect |
| 5. C2×#20263242 | C2 | semidirect |
| 6. #27160981 | C2 | semidirect |
| 7. C2×#104×C197 | C2 | semidirect |
| 11. #20263372 | C4 | semidirect |
| 19. C2×#15691342 | C22 | semidirect |
| 20. C2×C4⋊Dic197 | C22 | semidirect |
| 29. C2×M16×C197 | C22 | semidirect |
| 30. C2×C42×C197 | C22 | semidirect |
| 93. Dic394 | C22⋊C4 | semidirect |
| 100. D788 | C22⋊C4 | semidirect |
| 114. Q8×C197 | C22⋊C4 | semidirect |
| 118. D4×C197 | C22⋊C4 | semidirect |
| 165. C197 | #1792 | semidirect |
| 169. C2×#104 | D197 | semidirect |
| 187. C2×M16 | C2×D197 | semidirect |
| 190. C2×C42 | C2×D197 | semidirect |
| 263. Q8 | #15691335 | semidirect |
| 277. D4 | #15691335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263372 | 2 |
| C2×#20263254 | 2 |
| #27161081 | 2 |
| #27161080 | 2 |
| C2×#20263242 | 2 |
| #27160981 | 2 |
| C2×#104×C197 | 2 |
| #1792 | 197 |