Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 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. #27161115 | C2 | semidirect |
| 3. #27161095 | C2 | semidirect |
| 4. #27161053 | C2 | semidirect |
| 5. #27161052 | C2 | semidirect |
| 6. #27161037 | C2 | semidirect |
| 7. #421×C197 | C2 | semidirect |
| 13. C2×#15691348 | C4 | semidirect |
| 14. C2×#15691346 | C4 | semidirect |
| 15. C2×#15691345 | C4 | semidirect |
| 16. C2×#15691343 | C4 | semidirect |
| 132. C197 | #1976 | semidirect |
| 137. #421 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| #27161115 | 2 |
| #27161095 | 2 |
| #27161053 | 2 |
| #27161052 | 2 |
| #27161037 | 2 |
| #421×C197 | 2 |
| #1976 | 197 |