Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27163744 | C2 | semidirect |
| 5. #27163743 | C2 | semidirect |
| 6. #27163743 | C2 | semidirect |
| 7. #324×C199 | C2 | semidirect |
| 119. C199 | #1472 | semidirect |
| 127. #324 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263933 | 2 |
| #27163980 | 2 |
| C22⋊C8×D199 | 2 |
| #27163744 | 2 |
| #27163743 | 2 |
| #324×C199 | 2 |
| #1472 | 199 |