Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27164035 | C2 | semidirect |
| 3. #27164024 | C2 | semidirect |
| 4. #27164022 | C2 | semidirect |
| 5. #27164000 | C2 | semidirect |
| 6. #27163991 | C2 | semidirect |
| 7. #421×C199 | C2 | semidirect |
| 12. C2×#15691887 | C4 | semidirect |
| 18. C2×D4×D199 | C4 | semidirect |
| 19. C2×#15691870 | C22 | semidirect |
| 20. #20263914 | C22 | semidirect |
| 28. C2×M16×C199 | C22 | semidirect |
| 29. #117×C199 | C22 | semidirect |
| 153. C199 | #1795 | semidirect |
| 157. #421 | D199 | semidirect |
| 175. C2×M16 | C2×D199 | semidirect |
| 177. #117 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264001 | 2 |
| #27164035 | 2 |
| #27164024 | 2 |
| #27164022 | 2 |
| #27164000 | 2 |
| #27163991 | 2 |
| #421×C199 | 2 |
| #1795 | 199 |