Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #27160840 | C2 | semidirect |
| 5. #27160838 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. H(3,ℤ/4)×C197 | C2 | semidirect |
| 14. #20263283 | C4 | semidirect |
| 16. C42×D197 | C4 | semidirect |
| 102. C197 | #1827 | semidirect |
| 110. H(3,ℤ/4) | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161547 | 2 |
| #27161061 | 2 |
| #27161052 | 2 |
| #27160840 | 2 |
| #27160838 | 2 |
| #27160835 | 2 |
| H(3,ℤ/4)×C197 | 2 |
| #1827 | 197 |