Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C16×D199 | C2 | semidirect |
| 3. #107×D199 | C2 | semidirect |
| 4. #27163820 | C2 | semidirect |
| 5. #27163819 | C2 | semidirect |
| 6. #27163818 | C2 | semidirect |
| 7. #357×C199 | C2 | semidirect |
| 12. D8×D199 | C4 | semidirect |
| 15. C2×C199⋊C16 | C22 | semidirect |
| 17. #20263889 | C22 | semidirect |
| 20. C2×C16×C199 | C22 | semidirect |
| 21. #107×C199 | C22 | semidirect |
| 30. D1592 | C2×C4 | semidirect |
| 40. D8×C199 | C2×C4 | semidirect |
| 86. D199 | #357 | direct (N × H) |
| 87. C199 | C2×#357 | semidirect |
| 95. #357 | D199 | direct (N × H) |
| 106. C2×C16 | C2×D199 | semidirect |
| 109. #107 | C2×D199 | semidirect |
| 122. D8 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D199 | 2 |
| C2×C16×D199 | 2 |
| #107×D199 | 2 |
| #27163820 | 2 |
| #27163819 | 2 |
| #27163818 | 2 |
| #357×C199 | 2 |
| C2×#357 | 199 |