Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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. #27163839 | C2 | semidirect |
| 4. #27163838 | C2 | semidirect |
| 5. #364×C199 | C2 | semidirect |
| 54. C199 | #2153 | semidirect |
| 60. #364 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D199 | 2 |
| #27163972 | 2 |
| #27163839 | 2 |
| #27163838 | 2 |
| #364×C199 | 2 |
| #2153 | 199 |