Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #27160954 | C2 | semidirect |
| 5. #27160951 | C2 | semidirect |
| 6. #27160845 | C2 | semidirect |
| 7. #342×C197 | C2 | semidirect |
| 21. #20263240 | C4 | semidirect |
| 52. C22⋊Dic197 | C2×C4 | semidirect |
| 68. C22⋊C4×C197 | C2×C4 | semidirect |
| 73. C22×D197 | C4⋊C4 | semidirect |
| 94. C2×Dic197 | C4⋊C4 | semidirect |
| 157. C197 | #1867 | semidirect |
| 165. #342 | D197 | semidirect |
| 224. C22⋊C4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161552 | 2 |
| C2×#20263240 | 2 |
| #27160956 | 2 |
| #27160954 | 2 |
| #27160951 | 2 |
| #27160845 | 2 |
| #342×C197 | 2 |
| #1867 | 197 |