Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27161458 | C2 | semidirect |
| 5. #27160831 | C2 | semidirect |
| 6. #27160826 | C2 | semidirect |
| 7. #332×C197 | C2 | semidirect |
| 46. D788 | Q16 | semidirect |
| 78. C197 | #1669 | semidirect |
| 86. #332 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161458 | 2 |
| #27161360 | 2 |
| #27161356 | 2 |
| #27161144 | 2 |
| #27160831 | 2 |
| #27160826 | 2 |
| #332×C197 | 2 |
| #1669 | 197 |