Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161795 | C2 | semidirect |
| 2. #27161732 | C2 | semidirect |
| 3. #27161405 | C2 | semidirect |
| 4. #27161399 | C2 | semidirect |
| 5. #27161366 | C2 | semidirect |
| 6. #27161356 | C2 | semidirect |
| 7. #27161333 | C2 | semidirect |
| 8. C4×D1576 | C2 | semidirect |
| 9. #27161158 | C2 | semidirect |
| 10. #27161118 | C2 | semidirect |
| 11. #498×C197 | C2 | semidirect |
| 101. C8×C197 | #41 | semidirect |
| 127. C197 | #3354 | semidirect |
| 131. #498 | D197 | semidirect |
| 229. C8 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161795 | 2 |
| #27161732 | 2 |
| #27161405 | 2 |
| #27161399 | 2 |
| #27161366 | 2 |
| #27161356 | 2 |
| #27161333 | 2 |
| C4×D1576 | 2 |
| #27161158 | 2 |
| #27161118 | 2 |
| #498×C197 | 2 |
| #3354 | 197 |