Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27161209 | C2 | semidirect |
| 4. #27160830 | C2 | semidirect |
| 5. #27160811 | C2 | semidirect |
| 7. C82×C197 | C2 | semidirect |
| 59. C8×C197 | M16 | semidirect |
| 60. C8×C197 | SD16 | semidirect |
| 77. C197 | #1590 | semidirect |
| 85. C82 | D197 | semidirect |
| 137. C8 | #15691341 | semidirect |
| 138. C8 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161209 | 2 |
| C4×#15691347 | 2 |
| #27161158 | 2 |
| #27160830 | 2 |
| #27160811 | 2 |
| #27160808 | 2 |
| C82×C197 | 2 |
| #1590 | 197 |