Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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×#20263291 | C2 | semidirect |
| 4. #27161170 | C2 | direct (N × H) |
| 5. C2×#20263257 | C2 | semidirect |
| 6. C2×#20263251 | C2 | semidirect |
| 7. C2×C8×Dic197 | C2 | semidirect |
| 11. C2×#15691346 | C4 | semidirect |
| 15. #20263291 | C22 | semidirect |
| 23. #20263257 | C22 | semidirect |
| 24. #20263251 | C22 | semidirect |
| 25. C8×Dic197 | C22 | semidirect |
| 32. C2×Dic394 | C2×C4 | semidirect |
| 40. #15691346 | C2×C4 | semidirect |
| 41. C2×#13096802 | C2×C4 | semidirect |
| 63. Dic394 | C22×C4 | semidirect |
| 70. C2×Dic197 | SD16 | semidirect |
| 73. #13096802 | C22×C4 | semidirect |
| 104. Dic197 | C2×SD16 | semidirect |
| 106. C2×C197 | C4×SD16 | semidirect |
| 110. C197 | C2×C4×SD16 | semidirect |
| 217. C2 | #27161170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691346 | 2 |
| C2×#20263291 | 2 |
| C2×D4×Dic197 | 2 |
| #27161170 | 2 |
| C2×#20263257 | 2 |
| C2×#20263251 | 2 |
| C2×C8×Dic197 | 2 |
| C2×#102×C197 | 2 |
| C2×C4×SD16 | 197 |