Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 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×#15691348 | C2 | semidirect |
| 4. #27161318 | C2 | direct (N × H) |
| 5. C2×#20263259 | C2 | semidirect |
| 6. C2×#20263250 | C2 | semidirect |
| 7. C2×#20263249 | C2 | semidirect |
| 11. C2×#15691348 | C22 | semidirect |
| 21. #20263259 | C22 | semidirect |
| 22. #20263250 | C22 | semidirect |
| 23. #20263249 | C22 | semidirect |
| 75. C23×C197 | Q16 | semidirect |
| 99. C22×C197 | C2×Q16 | semidirect |
| 111. C2×C197 | #467 | semidirect |
| 115. C197 | C2×#467 | semidirect |
| 182. C23 | #15691348 | semidirect |
| 215. C22 | C2×#15691348 | semidirect |
| 227. C2 | #27161318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691348 | 2 |
| C23×#13096802 | 2 |
| C2×#20263305 | 2 |
| #27161318 | 2 |
| C2×#20263259 | 2 |
| C2×#20263250 | 2 |
| C2×#20263249 | 2 |
| C2×C22⋊Q8×C197 | 2 |
| C2×#467 | 197 |