Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
368 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27161641 | C2 | semidirect |
| 2. #27161213 | C2 | semidirect |
| 3. #27160812 | C2 | semidirect |
| 4. #27160803 | C2 | semidirect |
| 5. #392×C197 | C2 | semidirect |
| 13. C22⋊#13096802 | C22 | semidirect |
| 15. C22×D4×C197 | C22 | semidirect |
| 18. #95×C197 | C22 | semidirect |
| 21. C2×D788 | D4 | semidirect |
| 30. C4⋊Dic197 | D4 | semidirect |
| 68. C23×C197 | D8 | semidirect |
| 113. C197 | #1595 | semidirect |
| 117. #392 | D197 | semidirect |
| 122. C22×D4 | C2×D197 | semidirect |
| 132. #95 | C2×D197 | semidirect |
| 174. C23 | #15691343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161641 | 2 |
| #27161213 | 2 |
| #27160812 | 2 |
| #27160803 | 2 |
| #392×C197 | 2 |
| #1595 | 197 |