Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#20263883 | C2 | semidirect |
| 3. #27164020 | C2 | semidirect |
| 4. #27164019 | C2 | semidirect |
| 5. C2×#20263873 | C2 | semidirect |
| 6. #27163924 | C2 | semidirect |
| 7. C2×#104×C199 | C2 | semidirect |
| 11. #20264002 | C4 | semidirect |
| 154. C199 | #1793 | semidirect |
| 158. C2×#104 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264002 | 2 |
| C2×#20263883 | 2 |
| #27164020 | 2 |
| #27164019 | 2 |
| C2×#20263873 | 2 |
| #27163924 | 2 |
| C2×#104×C199 | 2 |
| #1793 | 199 |