Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27164071 | C2 | semidirect |
| 3. #27163763 | C2 | semidirect |
| 4. #27163761 | C2 | semidirect |
| 5. #432×C199 | C2 | semidirect |
| 80. C199 | #1553 | semidirect |
| 83. #432 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164568 | 2 |
| #27164071 | 2 |
| #27163763 | 2 |
| #27163761 | 2 |
| #432×C199 | 2 |
| #1553 | 199 |