Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊#13096802 | C2 | semidirect |
| 3. #27160945 | C2 | semidirect |
| 4. #27160841 | C2 | semidirect |
| 15. C4×D4×C197 | C4 | semidirect |
| 94. C197 | #1804 | semidirect |
| 105. C4×D4 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13096802 | 2 |
| C2×#20263247 | 2 |
| #27160945 | 2 |
| #27160841 | 2 |
| C2×C4×D4×C197 | 2 |
| #1804 | 197 |