Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27161132 | C2 | semidirect |
| 2. #27160945 | C2 | semidirect |
| 3. #27160813 | C2 | semidirect |
| 12. C4⋊Q8×C197 | C4 | semidirect |
| 13. #127×C197 | C4 | semidirect |
| 18. C4×D4×C197 | C4 | semidirect |
| 88. C197 | #1517 | semidirect |
| 95. C4⋊Q8 | Dic197 | semidirect |
| 96. #127 | Dic197 | semidirect |
| 101. C4×D4 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161132 | 2 |
| #27160945 | 2 |
| #27160813 | 2 |
| #532×C197 | 2 |
| #1517 | 197 |