Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161884 | C2 | semidirect |
| 2. #27161520 | C2 | semidirect |
| 3. #27161514 | C2 | semidirect |
| 4. #27161509 | C2 | semidirect |
| 5. C2×#20263269 | C2 | semidirect |
| 6. #27161496 | C2 | semidirect |
| 7. #578×C197 | C2 | semidirect |
| 12. #20263272 | C22 | semidirect |
| 13. #20263270 | C22 | semidirect |
| 14. #20263269 | C22 | semidirect |
| 15. #20263269 | C22 | semidirect |
| 16. #20263267 | C22 | semidirect |
| 17. #20263266 | C22 | semidirect |
| 18. C2×#15691333 | C22 | semidirect |
| 21. #135×C197 | C22 | semidirect |
| 22. C2×Q16×C197 | C22 | semidirect |
| 74. C197 | #3416 | semidirect |
| 76. #578 | D197 | semidirect |
| 88. #135 | C2×D197 | semidirect |
| 89. C2×Q16 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161884 | 2 |
| #27161520 | 2 |
| #27161514 | 2 |
| #27161509 | 2 |
| C2×#20263269 | 2 |
| #27161496 | 2 |
| #578×C197 | 2 |
| #3416 | 197 |