Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#20263345 | C2 | semidirect |
| 2. #27161749 | C2 | semidirect |
| 3. #27161733 | C2 | semidirect |
| 4. #27161451 | C2 | semidirect |
| 5. #27161307 | C2 | semidirect |
| 6. #27161290 | C2 | semidirect |
| 7. #27161242 | C2 | semidirect |
| 8. #27161221 | C2 | semidirect |
| 9. C4×#15691346 | C2 | semidirect |
| 10. #27161144 | C2 | semidirect |
| 11. #459×C197 | C2 | semidirect |
| 58. #15691346 | D4 | semidirect |
| 127. C4×C197 | #135 | semidirect |
| 140. C197 | #3284 | semidirect |
| 148. #459 | D197 | semidirect |
| 272. C4 | #20263345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263345 | 2 |
| #27161749 | 2 |
| #27161733 | 2 |
| #27161451 | 2 |
| #27161307 | 2 |
| #27161290 | 2 |
| #27161242 | 2 |
| #27161221 | 2 |
| C4×#15691346 | 2 |
| #27161144 | 2 |
| #459×C197 | 2 |
| #3284 | 197 |