Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 10. Q8×Dic199 | C4 | semidirect |
| 17. #20263879 | C4 | semidirect |
| 23. #103×C199 | C4 | semidirect |
| 71. Q8×C199 | C42 | semidirect |
| 109. C199 | #1763 | semidirect |
| 131. #103 | Dic199 | semidirect |
| 168. Q8 | C4×Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic199 | 2 |
| C2×#20263879 | 2 |
| C2×#20263865 | 2 |
| C4⋊C4×Dic199 | 2 |
| #27163781 | 2 |
| #27163780 | 2 |
| C2×#103×C199 | 2 |
| #1763 | 199 |