Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
438 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 113 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×#20263876 | C2 | semidirect |
| 3. C2×#20263875 | C2 | semidirect |
| 4. #27163920 | C2 | semidirect |
| 5. #27163780 | C2 | semidirect |
| 6. #27163773 | C2 | semidirect |
| 7. C2×C4×D4×C199 | C2 | semidirect |
| 11. C2×#15691871 | C4 | semidirect |
| 32. C2×D796 | C2×C4 | semidirect |
| 40. C2×C199⋊C8 | C2×C4 | semidirect |
| 91. D4×C199 | C22⋊C4 | semidirect |
| 101. C2×C4×C199 | D8 | semidirect |
| 146. C199 | #1879 | semidirect |
| 149. C2×C4×D4 | D199 | semidirect |
| 233. D4 | (C2×D199)⋊C4 | semidirect |
| 246. C2×C4 | #15691871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691871 | 2 |
| C2×#20263876 | 2 |
| C2×#20263875 | 2 |
| #27163920 | 2 |
| #27163780 | 2 |
| #27163773 | 2 |
| C2×C4×D4×C199 | 2 |
| #1879 | 199 |