Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 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. #27161122 | C2 | semidirect |
| 4. #27160948 | C2 | semidirect |
| 5. #27160848 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 15. #20263253 | C4 | semidirect |
| 31. #15691342 | C2×C4 | semidirect |
| 38. C4×Dic197 | C2×C4 | semidirect |
| 69. Q8×C197 | C4⋊C4 | semidirect |
| 73. D4×C197 | C4⋊C4 | semidirect |
| 112. C197 | #1859 | semidirect |
| 175. Q8 | #15691337 | semidirect |
| 179. D4 | #15691337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161122 | 2 |
| C2×#20263253 | 2 |
| #27161080 | 2 |
| #27160948 | 2 |
| #27160848 | 2 |
| #27160838 | 2 |
| #520×C197 | 2 |
| #1859 | 197 |