Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C22×#15691346 | C2 | semidirect |
| 2. C23×#13096802 | C2 | semidirect |
| 3. C2×#20263305 | C2 | semidirect |
| 4. #27161306 | C2 | direct (N × H) |
| 5. C2×#20263257 | C2 | semidirect |
| 6. C2×#20263249 | C2 | semidirect |
| 7. C2×#20263247 | C2 | semidirect |
| 11. C2×#15691346 | C22 | semidirect |
| 15. C22×#13096802 | C22 | semidirect |
| 17. #20263305 | C22 | semidirect |
| 21. #20263257 | C22 | semidirect |
| 22. #20263249 | C22 | semidirect |
| 23. #20263247 | C22 | semidirect |
| 40. C2×#13096802 | D4 | semidirect |
| 73. #13096802 | C2×D4 | semidirect |
| 80. C23×C197 | SD16 | semidirect |
| 107. C22×C197 | C2×SD16 | semidirect |
| 119. C2×C197 | #465 | semidirect |
| 123. C197 | C2×#465 | semidirect |
| 195. C23 | #15691346 | semidirect |
| 231. C22 | C2×#15691346 | semidirect |
| 243. C2 | #27161306 | 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 |
| C23×#13096802 | 2 |
| C2×#20263305 | 2 |
| #27161306 | 2 |
| C2×#20263257 | 2 |
| C2×#20263249 | 2 |
| C2×#20263247 | 2 |
| C2×#121×C197 | 2 |
| C2×#465 | 197 |