Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 2. #27161553 | C2 | semidirect |
| 3. #27161085 | C2 | semidirect |
| 4. #27161053 | C2 | semidirect |
| 5. #27160851 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. #421×C197 | C2 | semidirect |
| 11. C2×#15691345 | C4 | semidirect |
| 12. C2×#15691343 | C4 | semidirect |
| 37. C2×#13096802 | C2×C4 | semidirect |
| 49. C2×Q8×C197 | C2×C4 | semidirect |
| 51. C2×D4×C197 | C2×C4 | semidirect |
| 115. C197 | #1904 | semidirect |
| 119. #421 | D197 | semidirect |
| 146. C2×Q8 | C4×D197 | semidirect |
| 154. C2×D4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| #27161553 | 2 |
| #27161085 | 2 |
| #27161053 | 2 |
| #27160851 | 2 |
| #27160835 | 2 |
| #421×C197 | 2 |
| #1904 | 197 |