Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #27161487 | C2 | semidirect |
| 4. #27161486 | C2 | semidirect |
| 5. #27161480 | C2 | semidirect |
| 6. #27161476 | C2 | semidirect |
| 44. C2×#13096802 | Q8 | semidirect |
| 65. M16×C197 | Q8 | semidirect |
| 112. C197 | #3163 | semidirect |
| 159. M16 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161710 | 2 |
| #27161707 | 2 |
| #27161487 | 2 |
| #27161486 | 2 |
| #27161480 | 2 |
| #27161476 | 2 |
| #27161121 | 2 |
| #27161115 | 2 |
| C2×#20263257 | 2 |
| #27161037 | 2 |
| #428×C197 | 2 |
| #3163 | 197 |