Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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. #27164061 | C2 | semidirect |
| 4. C2×#20263874 | C2 | semidirect |
| 5. #27163925 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 120. C199 | #2038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164061 | 2 |
| C2×#20263882 | 2 |
| #27164019 | 2 |
| C2×#20263874 | 2 |
| #27163925 | 2 |
| #27163777 | 2 |
| #536×C199 | 2 |
| #2038 | 199 |