Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#20263974 | C2 | semidirect |
| 2. C2×#20263900 | C2 | semidirect |
| 3. C2×#20263896 | C2 | semidirect |
| 4. #27164255 | C2 | semidirect |
| 5. #27163821 | C2 | semidirect |
| 6. (C2×D199)⋊C16 | C2 | semidirect |
| 7. #357×C199 | C2 | semidirect |
| 32. Dic796 | D4 | semidirect |
| 43. D8×C199 | D4 | semidirect |
| 89. C199 | #2186 | semidirect |
| 96. #357 | D199 | semidirect |
| 128. D8 | D796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263974 | 2 |
| C2×#20263900 | 2 |
| C2×#20263896 | 2 |
| #27164255 | 2 |
| #27163821 | 2 |
| (C2×D199)⋊C16 | 2 |
| #357×C199 | 2 |
| #2186 | 199 |