Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27163980 | C2 | semidirect |
| 3. #95×D199 | C2 | semidirect |
| 4. #27163755 | C2 | semidirect |
| 5. #27163753 | C2 | semidirect |
| 6. #27163751 | C2 | semidirect |
| 7. #328×C199 | C2 | semidirect |
| 8. C2×#15691887 | C4 | semidirect |
| 13. #20263931 | C4 | semidirect |
| 14. #20263930 | C4 | semidirect |
| 19. #20263913 | C4 | semidirect |
| 31. C2×D796 | C2×C4 | semidirect |
| 46. C4⋊Dic199 | C2×C4 | semidirect |
| 53. C2×Q8×C199 | C2×C4 | semidirect |
| 58. C4⋊C4×C199 | C2×C4 | semidirect |
| 130. C199 | #1504 | semidirect |
| 136. #328 | D199 | semidirect |
| 160. C2×Q8 | C4×D199 | semidirect |
| 184. C4⋊C4 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164531 | 2 |
| #27163980 | 2 |
| #95×D199 | 2 |
| #27163755 | 2 |
| #27163753 | 2 |
| #27163751 | 2 |
| #328×C199 | 2 |
| #1504 | 199 |