Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27164058 | C2 | semidirect |
| 5. #27163779 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 7. #428×C199 | C2 | semidirect |
| 20. #20263871 | C4 | semidirect |
| 37. #15691870 | C2×C4 | semidirect |
| 51. M16×C199 | C2×C4 | semidirect |
| 114. C199 | #1856 | semidirect |
| 118. #428 | D199 | semidirect |
| 156. M16 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164492 | 2 |
| #27164058 | 2 |
| C2×#20263871 | 2 |
| #27163919 | 2 |
| #27163779 | 2 |
| #27163777 | 2 |
| #428×C199 | 2 |
| #1856 | 199 |