Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20263317 | C2 | semidirect |
| 3. #27161388 | C2 | semidirect |
| 4. #27161384 | C2 | semidirect |
| 5. #27161381 | C2 | semidirect |
| 6. #27161377 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161119 | C2 | semidirect |
| 9. #27161102 | C2 | semidirect |
| 135. C197 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263317 | 2 |
| #41×Dic197 | 2 |
| #27161388 | 2 |
| #27161384 | 2 |
| #27161381 | 2 |
| #27161377 | 2 |
| #27161121 | 2 |
| #27161119 | 2 |
| #27161102 | 2 |
| #27161080 | 2 |
| #417×C197 | 2 |
| #3080 | 197 |