Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
644 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 237 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×#20263326 | C2 | semidirect |
| 3. #27160985 | C2 | semidirect |
| 4. #27160977 | C2 | semidirect |
| 5. #27160949 | C2 | semidirect |
| 39. C22×C4×C197 | Q8 | semidirect |
| 77. C22×C197 | C4⋊Q8 | semidirect |
| 86. C4×C197 | C22⋊Q8 | semidirect |
| 95. C197 | #2857 | semidirect |
| 130. C22×C4 | Dic394 | semidirect |
| 173. C22 | #20263326 | semidirect |
| 184. C4 | #20263305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263326 | 2 |
| C2×#20263305 | 2 |
| #27160985 | 2 |
| #27160977 | 2 |
| #27160949 | 2 |
| #27160939 | 2 |
| C22×C42×C197 | 2 |
| #2857 | 197 |