Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. C22×#15691875 | C2 | semidirect |
| 2. C2×#20263934 | C2 | semidirect |
| 4. C2×#20263880 | C2 | semidirect |
| 5. C2×#20263877 | C2 | semidirect |
| 6. #27163781 | C2 | semidirect |
| 7. C2×C22⋊C8×C199 | C2 | semidirect |
| 35. C2×Dic398 | D4 | semidirect |
| 52. C4⋊Dic199 | D4 | semidirect |
| 70. C2×C8×C199 | D4 | semidirect |
| 102. C23×C199 | SD16 | semidirect |
| 157. C199 | #2000 | semidirect |
| 164. C2×C22⋊C8 | D199 | semidirect |
| 221. C2×C8 | C22⋊D199 | semidirect |
| 242. C23 | #15691875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691875 | 2 |
| C2×#20263934 | 2 |
| C2×#20263929 | 2 |
| C2×#20263880 | 2 |
| C2×#20263877 | 2 |
| #27163781 | 2 |
| C2×C22⋊C8×C199 | 2 |
| #2000 | 199 |