Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27164499 | C2 | semidirect |
| 3. C2×#20263883 | C2 | semidirect |
| 4. #27164023 | C2 | semidirect |
| 5. #27163787 | C2 | semidirect |
| 6. #27163778 | C2 | semidirect |
| 7. #390×C199 | C2 | semidirect |
| 10. #20263981 | C4 | semidirect |
| 42. #15691870 | C2×C4 | semidirect |
| 58. C2×D4×C199 | C2×C4 | semidirect |
| 69. Dic398 | C22⋊C4 | semidirect |
| 71. D796 | C22⋊C4 | semidirect |
| 132. C199 | #1883 | semidirect |
| 138. #390 | D199 | semidirect |
| 174. C2×D4 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263981 | 2 |
| #27164499 | 2 |
| C2×#20263883 | 2 |
| #27164023 | 2 |
| #27163787 | 2 |
| #27163778 | 2 |
| #390×C199 | 2 |
| #1883 | 199 |