Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. M16×Dic197 | C2 | semidirect |
| 5. C42×Dic197 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 7. #339×C197 | C2 | semidirect |
| 10. #20263291 | C4 | semidirect |
| 11. #20263288 | C4 | semidirect |
| 18. #20263254 | C4 | semidirect |
| 19. #20263252 | C4 | semidirect |
| 37. #15691342 | C2×C4 | semidirect |
| 45. C4×Dic197 | C2×C4 | semidirect |
| 51. M16×C197 | C2×C4 | semidirect |
| 57. C42×C197 | C2×C4 | semidirect |
| 60. Dic394 | C42 | semidirect |
| 62. D788 | C42 | semidirect |
| 101. Dic197 | #104 | semidirect |
| 107. C197 | C4×#104 | semidirect |
| 115. #339 | D197 | semidirect |
| 149. M16 | C4×D197 | semidirect |
| 165. C42 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161547 | 2 |
| C2×#20263254 | 2 |
| C2×#20263252 | 2 |
| M16×Dic197 | 2 |
| C42×Dic197 | 2 |
| #27160838 | 2 |
| #339×C197 | 2 |
| C4×#104 | 197 |