Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
310 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 51 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. #27164595 | C2 | semidirect |
| 2. #27164152 | C2 | semidirect |
| 3. #27163932 | C2 | semidirect |
| 4. #27163753 | C2 | semidirect |
| 5. #27163752 | C2 | semidirect |
| 6. #27163743 | C2 | semidirect |
| 7. #447×C199 | C2 | semidirect |
| 77. C2×Dic199 | D8 | semidirect |
| 134. C199 | #1598 | semidirect |
| 138. #447 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164595 | 2 |
| #27164152 | 2 |
| #27163932 | 2 |
| #27163753 | 2 |
| #27163752 | 2 |
| #27163743 | 2 |
| #447×C199 | 2 |
| #1598 | 199 |