Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #27161553 | C2 | semidirect |
| 3. #27161097 | C2 | semidirect |
| 4. #27161083 | C2 | semidirect |
| 5. #27161052 | C2 | semidirect |
| 6. #27160850 | C2 | semidirect |
| 7. H(3,ℤ/4)×C197 | C2 | semidirect |
| 12. C2×#15691347 | C4 | semidirect |
| 13. C2×D1576 | C4 | semidirect |
| 30. C2×Dic394 | C2×C4 | semidirect |
| 35. C2×D788 | C2×C4 | semidirect |
| 53. C2×C8×C197 | C2×C4 | semidirect |
| 115. C197 | #1904 | semidirect |
| 123. H(3,ℤ/4) | D197 | semidirect |
| 165. C2×C8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263354 | 2 |
| #27161553 | 2 |
| #27161097 | 2 |
| #27161083 | 2 |
| #27161052 | 2 |
| #27160850 | 2 |
| H(3,ℤ/4)×C197 | 2 |
| #1904 | 197 |