Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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×C22⋊(C199⋊C8) | C2 | semidirect |
| 3. C2×(C2×D199)⋊C8 | C2 | semidirect |
| 4. C2×C22⋊C8×C199 | C2 | semidirect |
| 12. C22×C199⋊C8 | C22 | semidirect |
| 16. C22×C8×C199 | C22 | semidirect |
| 22. C23×D199 | C8 | semidirect |
| 84. C22×C199 | C22⋊C8 | semidirect |
| 97. C2×D199 | C22⋊C8 | semidirect |
| 109. C199 | #1779 | semidirect |
| 114. C2×C22⋊C8 | D199 | semidirect |
| 124. C22×C8 | C2×D199 | semidirect |
| 202. C22 | (C2×D199)⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D199 | 2 |
| C2×C22⋊(C199⋊C8) | 2 |
| C2×(C2×D199)⋊C8 | 2 |
| C2×C22⋊C8×C199 | 2 |
| #1779 | 199 |