Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27164042 | C2 | semidirect |
| 3. C2×#20263873 | C2 | semidirect |
| 5. C4×M16×C199 | C2 | semidirect |
| 80. C199 | #1967 | semidirect |
| 86. C4×M16 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263943 | 2 |
| #27164042 | 2 |
| C2×#20263873 | 2 |
| C2×#20263871 | 2 |
| C4×M16×C199 | 2 |
| #1967 | 199 |