Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 2. C2×#20263253 | C2 | semidirect |
| 3. #27161083 | C2 | semidirect |
| 4. #27160980 | C2 | semidirect |
| 5. #27160848 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 7. #520×C197 | C2 | semidirect |
| 10. #20263351 | C4 | semidirect |
| 34. C2×D788 | C2×C4 | semidirect |
| 41. #15691342 | C2×C4 | semidirect |
| 84. Q8×C197 | C22⋊C4 | semidirect |
| 88. D4×C197 | C22⋊C4 | semidirect |
| 132. C197 | #1883 | semidirect |
| 135. #520 | D197 | semidirect |
| 208. Q8 | #15691335 | semidirect |
| 216. D4 | #15691335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C2×#20263253 | 2 |
| #27161083 | 2 |
| #27160980 | 2 |
| #27160848 | 2 |
| #27160838 | 2 |
| #520×C197 | 2 |
| #1883 | 197 |