Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 2. C2×#20263890 | C2 | semidirect |
| 3. #27164024 | C2 | semidirect |
| 4. #27164023 | C2 | semidirect |
| 5. C2×#20263871 | C2 | semidirect |
| 6. #27163976 | C2 | semidirect |
| 7. C2×#100×C199 | C2 | semidirect |
| 12. C2×#15691871 | C4 | semidirect |
| 111. C199 | #1978 | semidirect |
| 118. C2×#100 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691871 | 2 |
| C2×#20263890 | 2 |
| #27164024 | 2 |
| #27164023 | 2 |
| C2×#20263871 | 2 |
| #27163976 | 2 |
| C2×#100×C199 | 2 |
| #1978 | 199 |