Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27161845 | C2 | semidirect |
| 3. #27161084 | C2 | semidirect |
| 4. #27161052 | C2 | semidirect |
| 5. #27160836 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. #418×C197 | C2 | semidirect |
| 13. #20263322 | C4 | semidirect |
| 14. #20263313 | C4 | semidirect |
| 37. C2×#13096802 | D4 | semidirect |
| 56. C2×C8×C197 | D4 | semidirect |
| 115. C197 | #1910 | semidirect |
| 120. #418 | D197 | semidirect |
| 165. C2×C8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161845 | 2 |
| #27161646 | 2 |
| #27161084 | 2 |
| #27161052 | 2 |
| #27160836 | 2 |
| #27160835 | 2 |
| #418×C197 | 2 |
| #1910 | 197 |