Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #27164066 | C2 | semidirect |
| 4. M16×Dic199 | C2 | semidirect |
| 5. #27163788 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 15. #20263874 | C4 | semidirect |
| 16. #20263872 | C4 | semidirect |
| 95. C199 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164066 | 2 |
| C2×#20263882 | 2 |
| #27164002 | 2 |
| M16×Dic199 | 2 |
| #27163788 | 2 |
| #27163777 | 2 |
| #421×C199 | 2 |
| #1932 | 199 |