Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20263352 | C2 | semidirect |
| 2. C4×#15691358 | C2 | semidirect |
| 3. #27161276 | C2 | semidirect |
| 4. #27161271 | C2 | semidirect |
| 5. #27161103 | C2 | semidirect |
| 6. #27161084 | C2 | semidirect |
| 7. C2×#127×C197 | C2 | semidirect |
| 10. C2×#15691346 | C22 | semidirect |
| 11. C2×#15691343 | C22 | semidirect |
| 13. C4×Dic394 | C22 | semidirect |
| 14. C4×D788 | C22 | semidirect |
| 19. C4⋊#13096802 | C22 | semidirect |
| 20. #20263247 | C22 | semidirect |
| 28. #15691358 | D4 | semidirect |
| 59. Dic394 | C2×D4 | semidirect |
| 61. D788 | C2×D4 | semidirect |
| 94. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 104. C197 | #3038 | semidirect |
| 107. C2×#127 | D197 | semidirect |
| 201. C4 | #20263352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| C4×#15691358 | 2 |
| #27161276 | 2 |
| #27161271 | 2 |
| #27161103 | 2 |
| #27161084 | 2 |
| C2×#127×C197 | 2 |
| #3038 | 197 |