Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20263866 | C2 | semidirect |
| 3. C2×C4×C199⋊C8 | C2 | semidirect |
| 4. #27163773 | C2 | semidirect |
| 8. C22⋊(C199⋊C8) | C4 | semidirect |
| 77. C199 | #1750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C199⋊C8) | 2 |
| C2×#20263866 | 2 |
| C2×C4×C199⋊C8 | 2 |
| #27163773 | 2 |
| C2×#117×C199 | 2 |
| #1750 | 199 |